DS13 Abstracts · 100 DS13 Abstracts [email protected] CP4 Second Invariants for the...

96 DS13 Abstracts

IP1

Tire Tracks, the Stationary Schrodinger’s Equationand Forced Vibrations

I will describe a newly discovered equivalence between thefirst two objects mentioned in the title. The stationarySchrodinger’s equation, a.k.a. Hills equation, is ubiqui-tous in mathematics, physics, engineering and chemistry.Just to mention one application, the main idea of the Paultrap (for which W. Paul earned the 1989 Nobel Prize inphysics) amounts to a certain property of Hill’s equation.Surprisingly, Hill’s equation is equivalent to a seeminglycompletely unrelated problem of “tire tracks”. As a fur-ther surprise, there is a yet another connection betweenthe “tire tracks” problem and the high frequency forcedvibrations.

Mark LeviDepartment of MathematicsPennsylvania State [email protected]

IP2

Linear and Nonlinear Problems of MathematicalFinance

We start with a general overview of financial markets asdynamical systems and introduce primary financial assetsincluding bonds, equities, currencies, and commodities.Next, we give a broad outline of market microstructure,market impact, and algorithmic trading, with a particularemphasis of limit order books and their dynamics. We alsodiscuss technical trading and time-series analysis. Afterthat, we introduce financial derivatives and describe theirrisk-neutral and real-world valuation. We discuss possi-ble choices of stochastic processes used for modeling pri-mary assets; derive the corresponding pricing equations forderivatives, and demonstrate how these equations can besolved. We conclude our presentation by formulating someopen problems of mathematical finance.

Alexander LiptonBank of America Merrill Lynch &Imperial College London, United [email protected]

IP3

Particle Trajectories Beneath Irrotational Travel-ling Water Waves

We describe the pattern of the particle trajectories beneatha travelling wave moving at the surface of water in irrota-tional flow and with a flat bed, with no underlying current,both in the setting of periodic waves and in the setting ofsolitary waves.

Adrian ConstantinKing’s College London, United [email protected]

IP4

Triggered Slip Processes in Earth

In 1992, a magnitude 7.3 Landers earthquake occurred inSouthern California. As seismic waves were radiated, otherearthquakes were dynamically triggered both nearby andfar away, and elevated seismicity, termed delayed trigger-ing, lasted for several months. Recent observations basedon rapidly improving instrumentation show that a major-

ity of earthquakes may be dynamically triggered. Our workindicates that the granular physics of the fault core, faultgouge, plays a key role in triggering. Because direct accessto the fault is not possible, we are characterizing the granu-lar physics of triggering at laboratory scales using physicalexperiments and numerical simulations.

Paul JohnsonLos Alamos National Laboratory, [email protected]

IP5

Pattern Recognition with Weakly Coupled Oscilla-tory Networks

Traditional neural networks consist of many interconnectedunits and are thus inherently difficult to construct. In thelecture, we focus on neural network models of weakly cou-pled oscillators with time-dependent coupling. In thesemodels, each oscillator has only one connection to a com-mon support, which makes them predestinated for hard-ware implementation. Two coupling strategies are consid-ered. The first network was proposed by Hoppensteadt andIzhikevich [F.C: Hoppensteadt and E.M. Izhikevich, Phys.Rev. Lett. 82, 2983 (1999)] and possesses a global couplingfunction. The second one is a novel architecture with indi-vidual coupling functions. We present experimental real-izations of both networks and demonstrate that the devicescan reliably perform pattern recognition tasks. However,the scalability of the novel network architecture is muchsuperior to the one of the globally coupled oscillators.

Robert Holzel, Kathrin Kostorz, Katharina KrischerTechnische Universitat [email protected], [email protected],[email protected]

IP6

The Topology of Fluid Mixing

Topological chaos is a type of chaotic behavior that isforced by the motion of obstacles in some domain. I willreview two approaches to topological chaos, with applica-tions in particular to stirring and mixing in fluid dynamics.The first approach involves constructing devices where thefluid motion is topologically complex, usually by impos-ing a specific motion of stirring rods. I will then discussoptimization strategies that can be implemented. The sec-ond approach is diagnostic, where flow characteristics arededuced from observations of periodic or random orbitsand their topological properties. Many tools and conceptsfrom topological surface dynamics have direct applications:mapping class groups, braids, the Thurston-Nielsen classifi-cation theorem, topological entropy, coordinates for equiv-alence classes of loops, and the Bestvina-Handel algorithmfor train tracks.

Jean-Luc ThiffeaultDept. of MathematicsUniversity of Wisconsin - [email protected]

IP7

Modeling Reactive Events in Complex Systems

Reactive events such as conformation change of macro-molecules, chemical reactions in solution, nucleation eventsduring phase transitions, thermally induced magnetizationreversal in micromagnets, etc. pose challenges both for

DS13 Abstracts 97

computations and modeling. At the simplest level, theseevents can be characterized as the hopping over a free en-ergy barrier associated with the motion of the system alongsome reaction coordinate. Indeed this is the picture un-derlying classical tools such as transition state theory orKramers reaction rate theory, and it has been successful toexplain reactive events in a wide variety of context. How-ever this picture presupposes that we know or can guessbeforehand what the reaction coordinate of the event is.In many systems of interest – protein folding, enzyme ki-netics, protein-protein interactions, etc. – making sucheducated guesses is hard if not impossible. The questionthen arises whether we can develop a more general frame-work to describe reactive events, elucidate their pathwayand mechanism, and give a precise meaning to a conceptsuch as the reaction coordinate. In this talk I will discusssuch a framework, termed transition path theory, and in-dicate how it can be used to develop efficient algorithms toaccelerate the calculations and analysis of reactive events.

Eric Vanden-EijndenCourant InstituteNew York [email protected]

IP8

Predicting Epidemic Rare Events: A Dynami-cal Systems Perspective of Disease Extinction andControl

As seen by the many new vaccination campaigns across theworld, disease control is of paramount importance in pub-lic health with eradication as the ultimate goal. Withoutintervention, disease extinction in a large well mixed pop-ulation would be a rare event. In this talk, I will reviewsome of the mathematical models and machinery used todescribe the underlying dynamics of rare events in finitepopulation disease models. I will show how to derive anew dynamical model that includes a dynamical systemsdescription of the effective fluctuations of the noise thatdrives the disease to extinction. In analyzing the dynamictopology of the new expanded model, we can understandextinction from a dynamical systems perspective, thus dis-covering how to best use disease controlling resources.

Lora BillingsMontclair State UniversityDept. of Mathematical [email protected]

IP9

Engineered Gene Circuits: From Oscillators toSynchronized Clocks and Biopixels

This talk will focus on the development of synthetic geneoscillators and their synchronization. I will first describean engineered intracellular oscillator that is fast, robust,and persistent, with tunable oscillatory periods as fast as13 minutes. Experiments show remarkably robust andpersistent oscillations in the designed circuit; almost ev-ery cell exhibits large-amplitude fluorescence oscilla- tionsthroughout each experiment. Theory reveals that the keydesign principles for constructing a robust oscillator are asmall time delay in the negative feedback loop and enzy-matic protein decay that functions as an overloaded queue.I will then describe intercellular coupling that is used togenerate synchronized oscillations in a growing populationof cells. Microfluidic devices tailored for cellular popu-

lations are used to demonstrate collective synchronizationproperties along with spatiotemporal waves occurring onmillimeter scales. While quorum sensing proves to be apromising design strategy for reducing variability throughcoordination across a cellular population, the length scalesare limited by the diffusion time of the small molecule gov-erning the intercellular communication. I will concludewith recent progress engineering the synchronization ofthousands of oscillating colony biopixels over centimeterlength scales.

Jeff HastyUniversity of California, San [email protected]

SP1

Juergen Moser Lecture: Title to Be Announced

To be posted when available.

Nancy KopellBoston UniversityDepartment of [email protected]

CP1

A New, Braid-Theoretic Approach to UncoveringTransport Barriers

In oceanic settings, it is desirable to identify key transportbarriers that organize the material transport. In manycases the only velocity fields that are available for process-ing to find these barriers are geophysical models, whichmay not reliably represent the surface flow or the motionof particles on the ocean surface. In situations where thesurface velocity field is not reliably known, however, thereis the still the possibility of making direct measurements oftrajectories through tracking floats. We look to develop amethod that has the potential to harness this trajectory in-formation to identify the existence of transport barriers byusing tools from topology, in particular braid theory. Wewill present our braid theory based method and proceduresfor improving the accuracy of the resulting approximationfor the transport barrier location.

Michael AllshouseDept. of Mechanical EngineeringMassachusetts Institute of [email protected]

Thomas PeacockMassachusetts Institute of [email protected]


CP1

Development of An Efficient and Flexible Pipelinefor Lagrangian Coherent Structure Computation

The utility of Lagrangian coherent structures for advectivetransport analysis is well-established. Broader adoption ofthis method is facilitated by development of robust andflexible software elements that accommodate wide-rangingapplication areas, and modularity that is easily extended

98 DS13 Abstracts

or modified. We discuss use of Visualization Toolkit li-braries and standards as a foundation for object-orientedLCS computation, and how this facilitates integration withflow visualization softwares. We discuss GPU kernels for ef-ficient parallel computation, including optimization strate-gies for better utilization.

Shawn C. ShaddenCardiovascular Biomechanics Research LaboratoryStanford [email protected]

Sivash Ameli, Yogin DesaiIllinois Institute of [email protected], [email protected]

CP1

New Developments in LCS Theory: Forward-TimeUnstable Manifolds and Generalized Shearless Tori

The recent geodesic theory of Lagrangian coherent struc-tures (LCS) [Haller & Beron-Vera, Physica D 241 (2012)]has enabled the accurate computation of transport barriersin temporally aperiodic flows, including generalized stableand unstable manifolds, generalized KAM tori, and gener-alized shear jets. For two-dimensional flows, the remain-ing challenges in LCS detection include the computation ofgeneralized stable and unstable manifolds from a single nu-merical run, and the identification of generalized shearless(or twistless) KAM tori. In this talk, we present resultson both of these problems, and show their application tounsteady fluid flows.

Mohammad FarazmandPhD student, Mathematics, ETH [email protected]

Daniel BlazevskiDepartment of Mechanical and Process EngineeringETH [email protected]

George HallerETH, Zurich, [email protected]

CP1

Detecting Invariant Manifolds in AperiodicallyForced Mechanical Systems

We show how the recently developed theory of geodesictransport barriers for fluid flows can be used to uncoverkey invariant manifolds in externally forced, one-degree-of-freedom mechanical systems. Specifically, invariant sets insuch systems turn out to be shadowed by least-stretchinggeodesics of the Cauchy-Green strain tensor computedfrom the flow map of the forced mechanical system. Thisapproach enables the finite-time visualization of general-ized stable and unstable manifolds, attractors and general-ized KAM curves under arbitrary forcing, when Poincaremaps are not available. We illustrate these results by de-tailed visualizations of the key finite-time invariant sets ofconservatively and dissipatively forced Duffing oscillators.

Alireza HadjighasemResearch Assistant at McGill [email protected]

Mohammad Farazmand

PhD student, Mathematics, ETH [email protected]


CP1

Finite-time Scalar Reaction-diffusion with La-grangian Coherent Structures

In recent years, the concept of Lagrangian coherent struc-tures (LCS) has gained popularity in identifying finite-timeinvariant manifolds in aperiodic dynamical systems. Theyare relevant to quantifying the chaotic transport in non-diffusive fluid flows. In this talk, I will discuss some recentefforts on extending the use of LCS in systems with finitediffusion and reaction. It is found that in geophysicallyrelevant regimes, LCS closely relate to the variability ofscalar reaction-diffusion processes, suggesting its furtheruse beyond a diagnostic tool for chaotic transport.

Wenbo TangArizona State [email protected]

CP2

Steady Periodic Waves Bifurcating for Fixed-Depth Rotational Flows

We consider the existence of steady periodic water wavesfor rotational flows with a specified fixed-depth over a flatbed. We construct a modified height function which ex-plicitly introduces the mean-depth into the rotational wa-ter wave problem, and use the Crandall-Rabinowitz localbifurcation theorem to establish the existence of solutionsof the resulting problem. In the process we obtain explicitdispersion relations for the resulting flows.

David HenryUniversity of [email protected]

CP2

Revisiting the Two Wakes Interaction

this paper describes a model of two landau equations thatcaptures the interaction between the wakes of the incom-pressible flow between two cylinders in side by side arrange-ment. From the calculation of the stability problem in theproximity of the first Hopf bifurcation for this particulartype of flow, and an asymptotic approach appears this dy-namic system of two coupled Landau equations, which inour view captures the nonlinear dynamics of this type offlow.

Jose Ignacio H. LopezMackenzie Presbiterian University, Rua daConsolao, 930,Cep:01302-907, So Paulo, [email protected]

CP2

Cross-Waves Driven by Extended Forcing

The nonlinear Schrodinger equation models successfullyused to study cross-waves since Jones (JFM 138, 1984)rely on the assumption that modulations occur on a slowlengthscale compared to the subharmonic wavelength and

DS13 Abstracts 99

to the spatial extent of the forcing. Neither assumptionholds for high frequency (large aspect ratio) experiments.We extend the theory to include surface tension and a spa-tially extended forcing term and compare the resulting am-plitude equations with recent experiments, finding goodagreement.

Jeff Porter, Ignacio Tinao, Ana Laveron-SimavillaUniversidad Politecnica de [email protected], [email protected],[email protected]

CP2

Rayleigh Surface Wave in An IncompressibleEarths Crustal Layer Sandwiched Between a RigidBoundary Plane and a Half Space

In the present paper, Rayleigh surface wave in an earthscrustal layer has been studied. In the first case, the layerhas been kept sandwiched between a rigid boundary planeand a sandy half space, while in the second case the sandyhalf space has been replaced by an elastic half space withvoid pores. The dispersion relation has been deducedand the effect of sandy parameter, rigid boundary, wavenumber, inhomogeneity parameter and void parameter hasbeen illustrated and displayed by means of graphs.

Sumit K. VishwakarmaIndian School of Mines, Dhanbad, Jharkhand,[email protected]

CP3

Measurement and Validation of Coupled-PatchPopulation Models Via Computational Topology

Coupled patch models of population dynamics combine lo-cal dynamics on patches with rules for dispersal of the pop-ulation between patches. Thresholded population valuesgive rise to spatial patterns and may evolve in a compli-cated manner in time. I will discuss joint work with Ben-jamin Holman in which we study coupled Ricker maps andthe complicated patterns they produce. I will also presentpreliminary work on model construction and validation us-ing field measurements of population distribution and den-sity.

Sarah DayThe College of William and [email protected]

Jesse BerwaldCollege of William and [email protected]

CP3

Bifurcation Analysis of Reaction-Diffusion Vege-tation Pattern Formation Models for Semi-AridEcosystems

We consider a class of reaction-diffusion models that seek toexplain spatial vegetation patterns in semi-arid ecosystems.As a precipitation parameter is varied in these models, pat-terned states are created and destroyed in a pair of Turingbifurcations. The patterned states are characterized by upand down-hexagons on either side of a labyrinthine inter-mediate. We look at the transition between patterns usingbifurcation theory to identify generic scenarios for transi-

tions between these states.

Karna V. GowdaNorthwestern [email protected]

Mary SilberNorthwestern UniversityDept. of Engineering Sciences and Applied [email protected]

Hermann RieckeApplied MathematicsNorthwestern [email protected]

CP3

Highly Heteroclinically Connected PopulationModels

Modeling population dynamics using approximately con-served quantities facilitates analysis of phenomena drivenby unpredictable time-dependent factors (e.g. annual rain-fall). Level sets containing several saddle points linked byheteroclinic orbits can approximate complex behavior thatis poorly modeled by single equilibrium conservative mod-els such as Lotka-Volterra—small perturbations can triggerrapid, dramatic changes in qualitative dynamics. Highlyheteroclinic models fit to the well-known Isle Royale wolf-moose and Hudson Bay Company lynx-hare harvest datasuccessfully capture pivotal transitions.

Debra LewisDepartment of MathematicsUC Santa [email protected]

CP3

An Age-Structured Population Model with State-Dependent Delay: Derivation and Numerical Inte-gration

We present an age-structured population model that ac-counts for the following aspects of complex life cycles: (i)There are juvenile and adult stages, (ii) only the adult stageis capable of reproducing, (iii) cohorts of juveniles can tran-sition to the adult stage when they have consumed enoughnutrition and (iv) the juvenile and adult populations con-sume different limited food sources. Taking all of theseinto account leads to a new mathematical model that can-not be directly analyzed using the established framework offunctional differential equations or simulated by standardnumerical schemes for age-structured populations. My talkwill present the derivation of the model, its properties andnumerical scheme to integrate the equations.

Felicia MagpantayDept of Mathematics & StatisticsMcGill [email protected]

Nemanja KosovalicDepartment of Mathematics and StatisticsYork [email protected]

Jianhong WuDepartment of Mathematics and StatisticsYork University

100 DS13 Abstracts

[email protected]

CP4

Second Invariants for the Topological Characteri-zation of the Iteration of Differentiable Functions

We consider dynamical systems defined by a particularclass of differentiable functions, as fixed state space. Thedynamics is given by the iteration of an operator inducedby a polynomial map which belongs to an appropriate fam-ily of bimodal interval maps. We characterize topologicallythese dynamical systems, in particular using the second in-variants defined for the iteration of the bimodal intervalmaps.

Maria F. CorreiaUniversity of [email protected]

CP4

Bifurcation of Safe Sets in 1-Dimensional Dynami-cal Systems

Partial-control in dynamical systems is a relatively newconcept in which the trajectory is sought to be confinedwithin a compact set rather than made to follow a pre-scribed trajectory. Safe sets arise naturally in partial-control and are typically compact sets with interior anddepend on two parameters, the disturbance and controlbounds. Here, the change in safe sets in 1-dimensional sys-tems with changes in the parameters is studied and thesingularities classified and explained.

Suddhasattwa DasDepartment of MathematicsUniversity of Maryland, College [email protected]

CP4

Metric Entropy for Nonautonomous DynamicalSystems

In my talk, I introduce the notion of metric entropy fora nonautonomous dynamical system given by a sequence(Xn, μn) of probability spaces and a sequence of measur-able maps fn : Xn → Xn+1 with fnμn = μn+1. Thisnotion generalizes the classical concept of metric entropyestablished by Kolmogorov and Sinai, and is related via avariational inequality to the topological entropy of nonau-tonomous systems as defined by Kolyada, Misiurewicz andSnoha.

Christoph KawanInstitute of MathematicsUniversity of [email protected]

CP4

Graphical Krein Signature and Its Application toHamiltonian-Hopf Bifurcations

We present a new type of criterion for Hamiltonian-Hopfbifurcation, particularly exact conditions allowing or pre-venting a collision of eigenvalues of opposite Krein signa-ture. We give an exact condition contrary to the exist-ing work that only covers ’generic’ systems. The criterionarises from the geometrical theory of graphical Krein signa-ture. This is a joint work with Peter Miller (U Michigan).

Richard KollarComenius UniversityDepartment of Applied Mathematics and [email protected]

CP4

Two Linear Foci Suffice to Get Three Nested LimitCycles

By considering a specific family of discontinuous differen-tial systems with two linear zones sharing the equilibriumposition, strong numerical evidence about the existenceof three nested limit cycles was obtained very recently in[Huan, S.-M. and X.-S. Yang, On the number of limit cy-cles in general planar piecewise linear systems, Discreteand Continuous Dynamical Systems-A, 32 (2012), 2147–2164]. We show, thanks to the canonical forms introducedin [Freire, E., Ponce, E., and F. Torres, Canonical Discon-tinuous Planar Piecewise Linear Systems, SIAM J. AppliedDynamical Systems, 11 (2012), 181–211] how to prove inan analytical way the existence of such three limit cyclesin more general cases, by following a bifurcation approach.

Francisco Torres, Emilio FreireDepartamento Matematica Aplicada IIUniversidad de Sevilla, [email protected], [email protected]

Enrique PonceDepartamento de Matematica AplicadaEscuela Tecnica Superior de Ingenieros, Seville, [email protected]

CP5

Spinodal Decomposition for the Cahn-Hilliard-Cook Equation

We study the Cahn-Hilliard-Cook equation, which is amodel for a binary alloy. Spinodal decomposition in thismodel is described by different stages, based on the inter-play of linear solution, nonlinearity and stochastic forcing.It can be shown that initially the additive white noise de-termines the exact position of the patterns arising. Thecharacteristic features of the decomposed pattern are inde-pendent from the noise. After the initial stage the generaldynamics behaves mostly deterministic until the pattern isfully developed.

Philipp DurenUniversitat [email protected]

Dirk BlomkerUniversitat [email protected]

CP5

Localized Radial Solutions of the SwiftHohenbergEquation on the Poincare Disk

In this talk, we present a result of existence of stationarylocalized radial solutions of the Swift-Hohenberg equationon the real hyperbolic space of dimension two, that weidentify with the Poincare disk. This type of solutions

DS13 Abstracts 101

is of particular interest for some problems of orientationtuning in the visual cortex. The proof relies on spatialdynamics techniques. We also use numerical continuationto highlight our theoretical result.

Gregory FayeSchool of MathematicsUniversity of [email protected]

CP5

Fluctuations of Lyapunov Exponents in Space-Time Chaos: A Diffusion Process Linked to SurfaceRoughening

In a recent paper Kuptsov and A. Politi [Phys. Rev.Lett. 107, 114101 (2011)] reported on numerical simula-tions showing that the Lyapunov exponents fluctuationsscale with system size according to a universal scaling law.Here we show that both the power law scaling and theuniversal exponent can be deduced analytically from thescaling behavior of the characteristic (or covariant) Lya-punov vectors. In particular, we define a surface asso-ciated with each Lyapunov vector such that the surfaceturns out to be a fractal whose roughening exponents (i.e.fractal dimensions) are directly linked to the Lyapunovexponent fluctuation exponent through a universal scal-ing relation. We, therefore, uncover a profound connec-tion between the Lyapunov spectrum of (deterministic)chaotic spatially extended systems and the dynamics ofnon-equilibrium (stochastic) surfaces.

Juan M. Lopez

Instituto de Fisica de Cantabria (IFCA), [email protected]

Diego PazoInstituto de Fisica de Cantabria, [email protected]

Antonio PolitiInstitute for Complex Systems and Mathematical Biology,University of Aberdeen, [email protected]

CP5

Invariant Manifolds Describing the Dynamics ofa Hyperbolic-Parabolic Equation from NonlinearViscoelasticity

The governing equations for a collection of dynami-cal problems for heavy rigid attachments carried bylight, deformable, nonlinearly viscoelastic bodies are stud-ied. These equations are a discretization of a nonlinearhyperbolic-parabolic partial differential equation coupledto a dynamical boundary condition. A small parametermeasuring the ratio of the mass of the deformable body tothe mass of the rigid attachment is introduced, and geo-metric singular perturbation theory is applied to reduce thedynamics to the dynamics of the slow system. Fenichel the-ory is then applied to the regular perturbation of the slowsystem to prove the existence of a low-dimensional invari-ant manifold within the dynamics of the high-dimensionaldiscretization.

J. Patrick WilberDepartment of MathematicsUniversity of [email protected]

CP5

A Continuous Generalization of the Ising Model

Traditionally, ferromagnetism is studied from the stand-point of statistical mechanics, using the Ising model. Whileretaining the Ising energy arguments, we use techniquespreviously applied to sociophysics to propose a continuummodel. Our formulation results in an integro-differentialequation that allows for asymptotic analysis of phase tran-sitions, material properties, and the dynamics of the for-mation of magnetic domains.

Haley Yaple, Daniel AbramsNorthwestern [email protected],[email protected]

CP6

Reduction Methods for a Family of Infinite-dimensional Nonsmooth Energy Balance Models

We study a family of energy balance models that nu-merically exhibit sustained oscillations of canard andrelaxation-type. Although the full infinite-dimensional sys-tem can be reduced to a two-dimensional invariant mani-fold, one finds that within this manifold a slow-fast systemgoverns the dynamics and that the associated vector fieldis nonsmooth. The lack of smoothness is due to physicalassumptions on the system and results in a slow manifoldwhich is only piecewise smooth. In this talk, we introducetechniques for proving the existence of periodic orbits inthe full system in the presence of this difficulty.

Anna M. BarryInstitute for Mathematics and its ApplicationsUniversity of [email protected]

CP6

Effects of Noise on Grazing Bifurcations

In this talk I will describe the effects of incorporating noiseinto a canonical vibro-impacting model. An attractor ofthe deterministic model becomes an invariant density whennoise is added. Under parameter change, the density tran-sitions between approximately Gaussian and highly non-Gaussian forms. Impacts correspond to an extreme nonlin-earity and as a consequence the size of the invariant densitymay be proportional to the square-root of the noise ampli-tude.

David J. SimpsonDepartment of MathematicsUniversity of British [email protected]

John HoganBristol Centre for Applied Nonlinear MathematicsDepartment of Engineering Mathematics, University [email protected]

Rachel KuskeUniversity of British [email protected]

CP6

On Quasi-Periodic Perturbations of Hyperbolic-

102 DS13 Abstracts

Type Degenerate Equilibrium Point of a Class ofPlanar Systems

This paper considers two-dimensional nonlinear quasi-periodic system with small perturbations. Assume thatthe unperturbed system has a hyperbolic-type degenerateequilibrium point and the frequency satisfies the Diophan-tine conditions. By KAM iteration we prove that for suffi-ciently small perturbations, the system can be reduced toa suitable normal form with an equilibrium point at theorigin.

Junxiang XuSoutheast University, [email protected]

CP6

Infinitely Many Homoclinic Orbits for SuperlinearHamiltonian Systems

In this paper we study the first order nonautonomousHamiltonian System z? = JHz(t, z), where H(t, z) de-pends periodically on t. By using a generalized linkingtheorem for strongly indefinite functionals, we prove thatthe system has infinitely many homoclinic orbits for weaksuperlinear cases.

Wang JunJiangsu [email protected]

Junxiang Xu, Fubao ZhangSoutheast University, [email protected], [email protected]

CP7

Self-Organized Network Structure by Co-EvolvingDynamics Between Reaction-Diffusive Resourceson Nodes and Weighted Connections

We investigated a simple model of a co-evolving weightednetwork exhibiting a dissipative diffusion process of a re-source over a weighted network and resource-dependentevolution of the link weights. We demonstrate that thisinterplay between dynamics both on and of the network,yields an emergence of power-law distributions in both thequantities of the resource and the strengths of the links, ac-companied with a microscopic continuous evolution of thenetwork.

Takaaki AokiFaculty of EducationKagawa [email protected]

Toshio AoyagiGraduate School of InformaticsKyoto [email protected]

CP7

Oscillatory Network Turing Instability

Diffusion-induced instabilities in network-organized sys-tems are investigated. The oscillatory Turing instabilityis observed in three-component reaction-diffusion systems.In networks, the instability leads to spontaneous develop-ments of oscillations in a subset of nodes, depending on

the network architecture, while the other nodes continueto rest in the stationary steady state. Our results revealthat oscillations may occur even though individual nodesare not oscillators. This gives us a new scenario of oscilla-tory dynamics in network-organized systems.

Shigefumi HataNonliner Dynamics Group, Department of Physics,Graduate School of Sciences, Kyoto [email protected]

Hiroya NakaoGraduate School of Information Science and Engineering,Tokyo Institute of [email protected]

Alexander MikhailovComplex systems group, Department of PhysicalChemistry,Fritz-Haber-Institute of the [email protected]

CP7

Interplay Between Network Topology and Stabil-ity of a Linear Time Invariant (lti) Control Systemwith Homogeneous Delays

We focus on a class of LTI system with homogeneous inter-agent delays broadly studied in the literature, to presenthow the arising network structures (graphs) and delays arecorrelated from stability point of view, and how one candesign the graphs such that the network can tolerate largedelays without losing stability. We present these resultsbased on our Responsible Eigenvalue concept, analyticalstudy of rightmost eigenvalues and delay-adaptive inter-agent coupling design.

Wei QiaoNortheastern [email protected]

Rifat SipahiDepartment of Mechanical and Industrial EngineeringNortheastern [email protected]

CP7

The Joint Effect of Network Topology and UpdateFunctions on the Stability of Boolean Networks

Boolean networks are dynamical systems commonly usedto model gene regulation. We study the stability of at-tractors in a Boolean network with respect to small per-turbations. While recent work has addressed the separateeffects on stability of nontrivial network topology and up-date functions, only very crude information exists on howthese effects interact. We present a general solution whichincludes both effects, and we show that our predictionsagree with simulations of threshold Boolean networks.

Shane A. SquiresUniversity of MarylandInstitute for Research in Electronics and Applied [email protected]

Andrew PomeranceUniversity of Maryland–College [email protected]

DS13 Abstracts 103

Edward OttUniversity of MarylandInst. for Plasma [email protected]

Michelle GirvanUniversity of Maryland–College [email protected]

CP7

Large Systems of Interconnected Switches and Os-cillators

While networks of interacting dynamical systems are ofwidespread interest, most research has been restricted tosystems containing a single type of dynamical system (e.g.,coupled phase oscillators). We analyze large systems of in-terconnected oscillators and switches and find several co-existing stable solutions. Transitions between these steadystate solutions are explored, where we find that heterogene-ity may play an essential role in stabilizing the macroscopicdynamics of large complex systems.

Dane TaylorDepartment of Applied MathematicsUniversity of Colorado - [email protected]

Juan G. RestrepoDepartment of Applied MathematicsUniversity of Colorado at [email protected]

Elana FertigOncology BiostatisticsJohns Hopkins [email protected]

CP8

On the Role of Intrinsic Neuronal Dynamics forRelay Synchronization

Recently, a new form of synchronous behaviour has beendiscovered in a general context where two oscillators syn-chronize without being directly coupled, and the informa-tion transmission is going only via a third, relaying oscil-lator which is not synchronizing with the other ones (relaysynchronization). A thorough computational study of theeffect of different intrinsic dynamical states of Huber-Braunmodel neurons exhibiting relay synchronization under gap-junction coupling is presented.

Christian FinkeTheoretical Physics/Complex Systems GroupCarl-von-Ossietzky-Universitat [email protected]

Epaminondas RosaIllinois State UniversityDepartment of [email protected]

Hans BraunPhilipps University of Marburg, [email protected]

Ulrike FeudelUniversity of Oldenburg

ICBM, Theoretical Physics/Complex [email protected]

CP8

Suppression of Bursting Synchronization in Clus-tered Scale-Free Neuronal Networks

Functional brain networks are composed of cortical areasthat are anatomically and functionally connected. One ofthe cortical networks for which more information is avail-able is the cat cerebral cortex. Statistical analyses of thelatter suggest that its structure can be described as a clus-tered network, in which each cluster is a scale-free networkpossessing highly connected hubs. Those hubs are, on theirhand, connected together in a strong fashion (’rich-club’network). We have built a clustered scale-free networkinspired in the cat cortex structure so as to study theirdynamical properties. We focus on the synchronization ofbursting activity of the cortical areas and how it can besuppressed by means of neuron deactivation through suit-ably applied light pulses. It is possible to effectively sup-press bursting synchronization by acting on a single, yetsuitably chosen neuron, as long as it is higly connected,thanks to the ’rich-club’ structure of the network.

Ricardo L. VianaDepartmento de FisicaFederal University of [email protected]

Ewandson LameuGraduate Program in PhysicsState University of Ponta Grossa, [email protected]

Carlos BatistaDepartment of PhysicsFederal University of Parana, [email protected]

Antonio BatistaDepartment of Mathematics and StatisticsState University of Ponta Grossa, [email protected]

Kelly IaroszGraduate Program in PhysicsState University of Ponta Grossa, [email protected]

Sergio R. LopesDepartment of PhysicsFederal University of [email protected]

Juergen KurthsHumboldt Univ,Germany, Potsdam Institute for ClimateImpactResearch, Germany, and Aberdeen University, [email protected]

CP8

Optimal Chaotic Desynchronization and Its Appli-cation in Neural Populations

We develop a procedure which suggests a powerful alterna-tive to the use of pulsatile stimuli for deep brain stimulationtreatment of Parkinson’s disease. The procedure finds an

104 DS13 Abstracts

energy-optimal stimulus which gives a positive Lyapunovexponent, and hence desynchronization, for a neural pop-ulation, and only requires knowledge of a neuron’s phaseresponse curve, which can be measured experimentally. Weillustrate the procedure for a model for thalamic neurons,which are believed to play an important role in Parkinson’sdisease.

Dan D. WilsonMechanical EngineeringUniversity of California, Santa [email protected]

Jeff MoehlisDept. of Mechanical EngineeringUniversity of California – Santa [email protected]

CP8

Mathematical Models of Bidirectional Signaling inthe Neurovascular Unit

Neural network models can now simulate entire brain sec-tions resolved to individual cells. The roles of neurovas-cular and neuroglial interactions are less well understood.We have developed the first bidirectional model of the neu-rovascular unit, comprising synaptic discharge, glia, andarterioles. It is a mechanical, electrical, and biochemicalmodel with several interactional feedback loops. We willdescribe the biological system, model ODEs, and validationwith experimental literature.

Alix WitthoftBrown [email protected]

CP8

Limb Coordination in Crayfish Swimming: TheNeural Mechanisms and Mechanical Implications

During forward swimming, rhythmic movements of limbson different segments of the crayfish abdomen progressfrom back to front with the same period, but neighbor-ing limbs are phase-lagged by 25% of the period. Thiscoordination of limb movements is maintained over a widerange of frequency. The exact mechanisms underlying thisrobustly stable phase-locking are not known. We use dy-namical systems and fluid mechanics in conjunction withexperimental results to obtain insight into these mecha-nisms.

Calvin ZhangUniversity of California, [email protected]

Qinghai ZhangUniversity of [email protected]

Robert D. GuyMathematics DepartmentUniversity of California [email protected]

Brian MulloneyUniversity of California [email protected]

Timothy LewisDepartment of MathematicsUniversity of California, [email protected]

CP9

The Average Velocity of Planar Jordan Curves

We present a bound on the integral of the velocity ofa planar Jordan curve in the interior of another Jordancurve. This bound is applied to verify a new Poincare-Bendixson type result for planar infinite-horizon optimalcontrol. Namely, verifying the optimal value is attained bya periodic solution.

Ido BrightUniversity of [email protected]

Zvi ArtsteinThe Weizmann Institute of [email protected]

CP9

Bio-Inspired Sensing and Control of An Underwa-ter Vehicle in a Karman Vortex Street

By incorporating bio-inspired sensing modalities such asthose based on a fish lateral line system, underwater vehi-cles may be able to navigate complex, unknown environ-ments autonomously. This presentation describes resultsfrom using potential flow theory to model the flow arounda fish-like body in a Karman vortex street. Assuming sen-sors collect noisy measurements of the flow, a nonlinearobserver is incorporated to estimate the flow for use in afeedback controller designed for station-holding behavior.

Levi DeVries, Derek A. PaleyUniversity of MarylandDepartment of Aerospace [email protected], [email protected]

CP9

Amplitude Death Solutions for Stabilization ofDc Microgrids with Instantaneous Constant-PowerLoads

Constant-power loads on dc microgrids create a destabi-lizing effect on the circuit that can lead to severe voltageand frequency oscillations. Amplitude death is a couplinginduced stabilization of the fixed point of a dynamical sys-tem. We apply amplitude death methods to the stabiliza-tion problem in this constant-power setting. The ampli-tude death methods provide an open-loop control solutionto stabilize the system.

Stanley R. Huddy, Joseph SkufcaClarkson [email protected], [email protected]

CP9

ControllerSpace Categorization for Delay-Independent Sta-bility of Linear Time-Invariant (LTI) Systems withMultiple Uncertain Delays

In many dynamical systems, delays can be uncertain mak-ing their control difficult. For such systems, it would be

DS13 Abstracts 105

beneficial to design controllers that guarantee stability “in-dependent of delays’. On a general LTI system with multi-ple uncertain delays, we present a non-conservative frame-work to achieve this delay-independent stability (DIS) con-trol design even when the control matrices are structured.This framework is based on analysis of polynomials, al-though stability is associated with infinitely many eigen-values.

Payam M. NiaNortheastern [email protected]

Rifat SipahiDepartment of Mechanical and Industrial EngineeringNortheastern [email protected]

CP9

Branch and Bound Approach to the Optimal Con-trol of System Dynamics Models

The System Dynamics (SD) methodology is a frameworkfor modeling and simulating the dynamic behavior of so-cioeconomic systems. In order to optimally control suchdynamic systems, we propose a branch-and-bound ap-proach that is based on a) a bound propagation method,b) primal heuristics, and c) spatial branching on underly-ing nonlinear functions of the SD model. Our methods areimplemented in the MINLP solver SCIP. Numerical resultsfor test instances will be presented.

Ingmar VierhausZuse Institute [email protected]

Armin FugenschuhZuse Institut [email protected]

CP10

Cell Cycle Clustering in a Nonlinear MediatedFeedback Model

The concept of an RS type feedback model for Yeast Au-tonomous Oscillation is extended to include a mediatingchemical signaling agent. The dynamical properties of theresulting system include and extend previous results andmay explain the onset of spontaneous density-dependentoscillations seen in experiments.

Richard BuckalewOhio [email protected]

Todd YoungOhio UniversityDepartment of [email protected]

Erik BoczkoVanderbilt [email protected]

CP10

Period-Adding Cascades in Models of the Eukary-

otic Cell Cycle

Low-dimensional models of the eukaryotic cell cycle rep-resent cell division by discontinuous jumps in the modelstate, in response to the crossing of a protein concentra-tion below a critical level. This work documents period-adding cascades in such models, associated with conver-gent sequences of grazing bifurcations, and induced by thisjump discontinuity. It establishes the universal nature andscaling characteristics of such cascades in the unfolding ofsuitably constrained border-collisions and saddle-node bi-furcations of period-two orbits.

Harry DankowiczUniversity of Illinois at Urbana-ChampaignDepartment of Mechanical Science and [email protected]

Mike R. JeffreyUniversity of [email protected]

CP10

Dispersion and Breakup of Clusters in Cell CycleDynamics by Various Mechanisms

Random perturbations of the cell-cycle dynamics with feed-back model tend to disperse clusters. We consider andcontrast the effects of mechanisms of stochastic perturba-tions, variable division time and generational differenceson dispersion and eventual breakup of the clusters in thefeedback model. Beginning with numerical simulations, westudy the differences in the effects of these three types ofperturbations in the system in the setting of both smalland large perturbations.

Xue GongOhio [email protected]


Alexander NeimanDepartment of Physics and AstronomyOhio [email protected]

Richard BuckalewOhio [email protected]

Erik M. BoczkoDepartment of Biomedical InformaticsVanderbilt University Medical [email protected]

CP10

Universality of Stable Periodic Solutions in a CellCycle Mode

We study a model of cell cycle ensemble dynamics from theperspective of parameter space - a two dimensional triangleT . For the type of system consider and any positive inte-ger k there exists a special periodic solution that we callk-cyclic. We show under very general nonlinear feedback

106 DS13 Abstracts

that for a given k the stability of the k cyclic periodic solu-tions can be characterized completely in parameter space.For a given k we prove that T is partitioned into k2 sub-triangles on which k cyclic solutions all have the same sta-bility. We observe that for negative feedback parameterspace is nearly fully covered by regions of stability of kclustered solutions with k small, e.g. k ≤ 7. For manyparameter values we observe bi-stability or multi-stability.We also observe that as k grows large, the parameter re-gion for which the k cyclic solution is stable becomes smallin area and tends to the boundaries of parameter space.

Gregory MosesOhio [email protected]

CP10

On Cyclin/cdk Oscillations in the Cell Cycle

Abstract: The cell cycle is driven by complexes formedfrom cyclin dependent kinases (CDKs) and their cyclinsubunits (Clb2). Exiting mitosis requires a shift of balancebetween Clb2:CDK1 and the phosphatase Cdc14. Exper-iments show that Cdc14 can be locked in an oscillatoryregime by stabilising Clb2. Using a model we propose thatCdc14 being part of a biochemical oscillator increases itstunability, and Clb2 acting as a feedback controller leadsto increased robustness of Cdc14 activation.

Thomas ToddUniversity of [email protected]

CP11

Calculating Early Treatment Gains

The setting is a patient infected with a proliferatingpathogen. We consider the problem of calculating thedifference in time to resolution for the same interven-tion/adjuvant applied at two different times. Our goal isto develop a framework with which it is possible to regressthe early treatment gain from a minimal set of data.


Todd YoungDepartment of MathematicsOhio [email protected]

CP11

On Spread of Phage Infection of Bacteria in a PetriDish

A reaction diffusion system with time delay is proposed forvirus spread on bacteria immobilized on an agar-coatedplate. The delay explicitly accounts for a virus latent pe-riod. The focus is on the speed of spread of infection result-ing from a localized inoculum of virus and of the existenceof traveling waves of infection.

Hal L. SmithArizona state [email protected]

Horst ThiemeArizona [email protected]

Don JonesArizona State UniversityDepartment of [email protected]

CP11

A Perspective on Multiple Waves of Influenza Pan-demics

The past four influenza pandemic outbreaks in the UnitedStates has had multiple waves of infections, although theunderlying mechanisms are uncertain. We use mathemat-ical models to exhibit four mechanisms each of which canquantitatively reproduce the two waves of the 2009 H1N1pandemic. All models indicate that significantly reduc-ing or delaying the initial numbers of infected individualswould have little impact on the attack rate. This reductionor delay results in only one wave.

Howard WeissGeorgia [email protected]

CP11

The Significance of Hiv Modelling on Public HealthStrategies

It has been widely reported that new public health strate-gies have had a significant impact on decreasing new in-fection rates for HIV - in regions where the approach hasbeen implemented. In 2011 the journal Science declaredthat the biggest scientific breakthrough of the year wasthe new approach to HIV. I will explain how mathematicalmodelling of HIV transmission dynamics has played a sig-nificant role (possibly negative) in controlling the spread ofHIV. My work on HIV is joint with Brandy Rapatski andFred Suppe.

James A. YorkeUniversity of MarylandDepartments of Math and Physics and [email protected]

CP11

The Heterogeneous Dynamics of the TranscriptionFactor NF-kB

NF-kB is a transcription factor that controls hundreds ofgenes. Single-cell imaging has shown that when certainstimuli hit the cell, NF-kB nuclear concentration oscillates.Our experiments show that NF-kB dynamics in cells ismore heterogeneous than previously reported: in partic-ular, for some cells oscillations are not observed. We at-tempt to unveil the origin of this heterogeneity using amathematical model involving the main components of thesystem.

Samuel ZambranoSan Raffaele [email protected]

Marco E. BianchiSan Raffaele University, Milan (Italy)[email protected]

DS13 Abstracts 107

Alessandra AgrestiSan Raffaele Research Institute, Milan (Italy)[email protected]

CP12

An Approach to Secure Communication in ChaoticSystems Without Synchronization

The secure communication is important for several pur-poses, for example, to keep safe: banking sites, governmentsecrecy, ... A traditional way to build a secure communi-cation system is through the synchronization, instead of itwe present a novel feature without use synchronization asthe coding mechanism. In this work we will show how thetransfer entropy can be use to determine the coupling di-rections in coupled map lattices and then transmit secureinformation.

Fabiano FerrariUniversidade Federal do [email protected]


Romeu Szmoski, Sandro PintoUniversidade Estadual de Ponta [email protected], [email protected]

CP12

The Approximation of Coherent Structures in Non-Autonomous Dynamical Systems

Coherent structures in the context of non-autonomous dy-namical systems can be analyzed using transfer operatormethods based on long-term simulations of trajectories onthe whole state-space. In principal these methods are alsoapplicable to a part of the state-space. In this talk wepresent an algorithm that automatically selects a subsetof the state-space probably containing coherent structures.This preselection is based on the approximation of almostinvariant sets and reduces the numerical effort significantly.

Christian HorenkampChair of Applied MathematicsUniversity of [email protected]

Michael DellnitzUniversity of Paderborn, [email protected]

CP12

Autosynchronization Methods for Pde Model Fit-ting and Nonlinear Data Assimilation for OceanEcology Informed by Partially-Observed Hyper-spectral Satellite Imagery

Applications of synchronization to modeling ocean ecol-ogy by partially observed cloud-covered satellite imageryare discussed. When modeling spatiotemporal systems forwhich not all variables are observable, often the observ-able contains still hidden regions. Given multiple imagesof a dynamic scene and assumed model describing chaoticreaction diffusion dynamics, parameters and model statesare adaptively observed by synchronization of the model

to observed data, a specialized autosynchronization. Au-tosynchronization is effective despite hidden spatial infor-mation.

Sean KramerClarkson [email protected]

CP12

Monitoring the State of in-Land and Coastal Wa-ters from Space

I’ll describe current multi- and hyper-spectral imagers cur-rently used to examine water quality of coastal and in-landsites such as the Columbia River Mouth or Lake Erie. Be-sides showing many beautiful images, I’ll also provide anoverview of the current ’product’ algorithms used to es-timate geo-chemical-bio water parameters such as chloro-phyll concentration. I’ll further describe some new productalgorithms based on insights from nonlinear dynamics de-signed to capture the ’shape’ of ocean and lake color.

Nicholas Tufillarodynamic penguin, [email protected]

CP13

Multiple Snaking Scenarios in Three-DimensionalDoubly Diffusive Convection

Doubly diffusive convection is a classic example of apattern-forming system. Among the variety of solutionsexhibited by systems of this type are the interesting time-independent spatially localized states called convectons.Here, we focus on a three-dimensional binary fluid in avertically extended cavity with no-slip boundary conditionswhose motion is driven by temperature and concentrationdifferences between a pair of opposite vertical walls. No-flux boundary conditions are imposed on the remainingwalls. When the temperature and concentration contribu-tions to buoyancy balance the system admits a conduc-tion state whose instability leads to quasi two-dimensionalspatially localized rolls with D2 symmetry located on apair of primary snaking branches. Secondary symmetrybreaking instabilities occur during every nucleation pro-cess along the primary snaking branches and lead to fullythree-dimensional twisted convectons with Z2 symmetrywhich also snake.

Cedric BeaumeDepartment of PhysicsUniversity of California, [email protected]

Alain BergeonUniversite de Toulouse (France)[email protected]

Edgar KnoblochUniversity of California at BerkeleyDept of [email protected]

CP13

Localized Pattern Formation in Reaction DiffusionEquations with a Source Term

In this talk we will show how the theory of localized pat-

108 DS13 Abstracts

tern formation, via so-called homoclinic snaking arises nat-urally in systems of reaction diffusion equations in param-eter regimes where Turing instabilities occur. The key cri-terion is that the Turing instability should be sub-critical.We shall show how this situation arises naturally in aSchnakenberg system with a constant source term. Thisleads to an interplay between quadratic and cubic nonlin-ear terms when the problem is re-centered on the nontrivialequilibrium. For an appropriate set of parameter values, ofrelevance to a problem in plant biology, the restabilizationof the bifurcating branches leads to a snaking-like structurewhose dynamics can also be described using the theoryof semi-strong interaction. This provides a link betweenasymptotic theories of non-local spike interaction and un-derlying local Turing bifurcations.

Alan R. Champneys, Victor Brena-MedinaUniversity of [email protected],[email protected]

CP13

Spatial Localization in Two-Dimensional Convec-tion with a Large Scale Mode

Localized states (LS) are of considerable interest in bothrotating convection [C. Beaume et al., J. Fluid Mech.,in press (2012)] and magnetoconvection [D. Lo Jacono,A. Bergeon and E. Knobloch, J. Fluid Mech. 687, 595(2011)]. In 2d convection with stress-free boundary condi-tions (BCs), the formation of LS is due to the interactionbetween convective rolls and a large scale mode. We de-velop a fifth order nonlocal Ginzburg-Landau theory [H.-C.Kao and E. Knobloch], in preparation to describe the ef-fects of spatial modulation near a cod-2 point where theleading order theory breaks down [C. Beaume et al., J.Fluid Mech., in press (2012)]. With mixed velocity BCsthe large scale mode becomes (weakly) damped and a newlength scale appears in the problem. This permits the in-terpolation between global and local coupling and shedslight on numerical continuation results for 2d rotating con-vection with stress-free and no-slip BCs.

Hsien-Ching KaoUniversity of California at Berkeley, Department [email protected]

Cedric BeaumeDepartment of PhysicsUniversity of California, [email protected]


Alain BergeonUniversite de Toulouse (France)[email protected]

CP13

Phase Reduction Analysis of Oscillatory Patternsin Reaction-Diffusion Systems

Phase reduction method for oscillatory spatiotemporal dy-namics of reaction-diffusion systems, such as localizedspots, spiral waves, and target patterns, is developed.

Phase sensitivity function of the system, which quanti-fies linear phase response of the system to weak spatialperturbations, is obtained as the solution of an appropri-ate adjoint equation. Layers of coupled reaction-diffusionsystems exhibiting oscillatory dynamics are analyzed us-ing the developed method, and interesting synchronizationphenomena, such as multi-modal phase locking, are found.


Tatsuo YanagitaOsaka Electro-Communication [email protected]

Yoji KawamuraThe Earth Simulator CenterJapan Agency for Marine-Earth Science and [email protected]

CP13

Eisenman2012 Arctic Sea Ice Model: Analysis inDiscontinuous Albedo Limit

We analyze the Eisenman (2012) version of a low-dimensional Arctic sea ice model, developed to investigateArctic sea ice retreat under increasing greenhouse gases. Itincludes sea-ice thermodynamics, albedo feedback, and pe-riodic solar forcing, and is piecewise smooth. In the limit ofa discontinuous albedo, a Poincare map can be derived andanalyzed exactly to determine stability boundaries for itsfixed points. This approximation also introduces dynamicsassociated with Filippov piecewise-smooth systems, whichwe explore.

Kaitlin Speer, Mary SilberNorthwestern [email protected], [email protected]

CP14

Understanding Cellular Architecture in CancerCells

Progression to cancer causes a complex set of transforma-tions in a cell. Neoplastic cells are known to display markedchanges in the morphology of their organelles. However,there is still no clear mechanistic understanding of thistransformation process. We present a dynamical systemsapproach for the evolution of organelles morphology in can-cer cells. The results provided by this work may increaseour insight on the mechanism of tumorigenesis and helpbuild new therapeutic strategies.

Simone Bianco, Yee-Hung Mark ChanUC, San [email protected], [email protected]

Susanne RafelskiUC, [email protected]

Morgan Truitt, Wallace Marshall, Davide RuggeroUC, San [email protected], [email protected],[email protected]

DS13 Abstracts 109

Chao TangPeking University and UC, San [email protected]

CP14

Structural Adaptation of a Microvascular Network

The cardiovascular network provides oxygen and other nu-trients and removes waste from tissue. Network structureand function are thought to be maintained by vascularadaptation, the geometric structural change of microves-sels in response to hemodynamic and metabolic stimuli -abnormal vascular adaptation is thought to be associatedwith conditions such as hypertension, diabetes, and obe-sity. In this presentation we examine the dynamics of anadaptation model in a small network, and demonstrate thatbistability and limit cycles are to be expected.

John B. Geddes, Elizabeth Threlkeld, Margaret-AnnSegerFranklin W. Olin College of [email protected],[email protected],[email protected]

Rachel NancollasUC [email protected]

Alisha SieminskiOlin [email protected]

CP14

Robustness of Gene Regulatory Networks

The global dynamics of gene regulatory networks areknown to show robustness to perturbations of differentkinds: intrinsic and extrinsic noise, as well as mutationsof individual genes. One molecular mechanism underlyingthis robustness has been identified as the action of so-calledmicroRNAs that operate via different types of feedforwardloops. We will present results of a computational study,using the modeling framework of generalized Boolean net-works, that explores the role that such network motifs playin stabilizing global dynamics.

Claus KadelkaVirginia Bioinformatics Institute, Virginia [email protected]

David MurrugarraSchool of Mathematics, Georgia [email protected]

Reinhard LaubenbacherVirginia [email protected]

CP14

Chemical Signal Processing for Biological MagneticSensors

Geomagnetic fields measurably affect some animals be-havior but the mechanisms are poorly understood. In aleading theory supported by some experiments, quantum-mechanical oscillation modulates chemical reactions that

are sensitive to angular momentum. To thoroughly probethis theory, one must consider downstream chemical re-actions which may process photic and magnetic stimuli incomplicated ways. Toward this, we consider singular chem-ical dynamics perturbed by coherent oscillation, both in thedeterministic (thermodynamic) limit and with fluctuation.

Gregory A. RobinsonUniversity of Colorado at BoulderUniversity of California, [email protected]

CP14

Stability and Hopf Bifurcation in a MathematicalModel for Erythropoiesis

We consider an age-structured model for erythropoiesisthat describes the production of blood cells under the influ-ence of the hormone erythropoietin. Hemoglobin and ery-thropoietin are involved in a negative feedback loop. Wereduce the model to a system of two nonlinear ordinarydifferential equations with two constant delays for whichwe show existence of a unique steady state. We deter-mine all instances at which this steady state loses stabilityvia a Hopf bifurcation and establish analytical expressionsfor the scenarios in which these arise. We show examplesof supercritical Hopf bifurcations for parameter values es-timated according to physiological values and present nu-merical simulations in agreement with the theoretical anal-ysis. We provide a strategy for parameter estimation tomatch empirical measurements and compare existing dataon hemoglobin oscillation in rabbits with predictions of ourmodel.

Susana SernaDepartment of MathematicsUniversitat Autonoma de [email protected]

CP15

Chaotic Sickle Cell Blood Flow

Sickle cell blood flow is governed by the Navier-Stokes andoxygen transport equations. For an assumed time varyingsolution, neglecting higher order terms, non-linear PDEsare transformed to autonomous ODEs and related alge-braic equations. Fixed points, eigenvalues, and Lyapunovexponent for the ODEs are calculated. Computed deter-ministic, aperiodic, and initial condition sensitivity of theODEs show the chaotic nature of sickle cell blood flow.

Louis C. Atsaves, Wesley HarrisMassachusetts Institute of [email protected], [email protected]

CP15

Multistable Dynamics in Electroconvecting LiquidCrystals

By using a timescale separation algorithm based on diffu-sion map delay coordinates we have identified a small num-ber of multistable dynamical states in a small, 30 m wide,electroconvecting liquid crystal sample. These dynamicsare categorized by the repetitive formation, propagation,and annihilation of instabilities, or defects, in the sample.By perturbing the applied voltage at different phases ofthis defect cycle we are able to steer the system between

110 DS13 Abstracts

different multistable states.

Zrinka Greguric FerencekGeorge Mason [email protected]

John CressmanGeorge Mason UniversityKrasnow [email protected]

Tyrus BerryGeorge Mason [email protected]

Timothy SauerDepartment of MathematicsGeorge Mason [email protected]

CP15

Marangoni Oscillations in Rehology of LangmuirPolymer Monolayers

The dynamics of monolayers is important in a wide varietyof scientific and technological fields. In the case of Lang-muir polymer monolayers, experiments are commonly per-formed to measure surface rheological properties on whichthe dynamics is strongly dependent. In these experimentalconfigurations, a shallow liquid layer is slowly compressedand expanded in periodic fashion by moving two solid bar-riers, changing the free surface area and simultaneouslymeasuring surface properties. Since the forcing frequencyis small, current theoretical studies only include surfacephenomena while ignoring fluid dynamics in the bulk. Thisapproximation provides good results only if the dynamics issufficiently slow. Here we present a long wave theory thatdoes take fluid dynamics into account. This addresses theissue of flow effects in the measurement of surface prop-erties and allows one to determine how small oscillationfrequencies should be to obtain accurate values of rheolog-ical properties.

Maria HigueraE. T. S. I. AeronauticosUniv. Politecnica de [email protected]

Jose M. PeralesE. T. S. I. AeronauticosUniv. Politecnica de [email protected]

Jose VegaE. T. S. I. AeronauticosUniversidad Politecnica de [email protected]

CP15

Nonlinear Stability Analysis of Convective Rolls inGranular Fluid

In this talk we focus on granular convection. The granularconvection resembles Rayleigh Benard convection as bothare induced by the gravity and the temperature gradient.The linear stability analysis shows that the conduction be-comes unstable above the critical parameters which triggerconvection. The nonlinear stability analysis, around the

critical parameters, predicts that the transition from con-duction to convection state is via a supercritical bifurcationand this result agrees well with classical convection.

Priyanka ShuklaJNCASR, [email protected]

Meheboob AlamEngineering Mechanics UnitJNCASR, Jakkur P.O., Bangalore, [email protected]

CP15

Front Propagation in Steady Cellular Flows: ALarge-Deviation Approach

We examine the propagation speed of Fisher–Kolmogorov–Petrovskii–Piskunov chemical fronts in steady cellularflows. A number of predictions have previously been de-rived assuming small molecular diffusivity (large Pecletnumber) and either slow (small Damkohler number) or fast(large Damkohler number) reactions. Here, we employ thetheory of large deviations to obtain an eigenvalue problemwhose matched-asymptotics solution provides a descriptionof the front speed for all Damkohler values. Earlier resultsare recovered as limiting cases.

Alexandra TzellaDAMTP, [email protected]

Jacques VannesteSchool of MathematicsUniversity of [email protected]

CP16

Controlling Macroscopic Chaos in a Network ofCoupled Oscillators

A non-autonomous infinite network of coupled oscillatorscan exhibit chaos. We derive a reduction that accuratelydescribes its collective asymptotic behavior and design acontrol scheme based on this reduced system. The strategyis then applied to a finite network. Three examples arestudied: a bimodal Kuramoto system, a network of thetaneurons, and a network of Josephson junctions. We alsoexamine robustness with respect to the network size andrandom link removal.

Alexandre WagemakersUniversidad Rey Juan [email protected]

Ernest BarretoGeorge Mason UniversityKrasnow [email protected]

Miguel A.F. SanjuanUniversidad Rey Juan [email protected]

Paul SoGeorge Mason University

DS13 Abstracts 111

The Krasnow [email protected]

CP16

Designing Pulse Coupled Oscillators

Pulse coupled oscillators have numerous real world applica-tions in biology, and increasingly, applications in the con-trol of and synchronization of system clocks. We describea class of oscillators which mix excitation and inhibition aswell as change their own frequencies so as to synchronizerobustly, even when there is a complex network structure,time delays and heterogeneous oscillator frequencies. Wepresent both numerical and analytical arguments for thishighly non-linear system.

Joel D. Nishimura, Eric FriedmanCornell [email protected], [email protected]

CP16

Synchronous Dynamics and Bifurcation Analysis inTwo Delay Coupled Oscillators with Recurrent In-hibitory Loops

In this study, the dynamics and low-codimension bifurca-tion of the two delay coupled oscillators with recurrentinhibitory loops are investigated. We discuss the abso-lute synchronization character of the coupled oscillators.Then the characteristic equation and the possible low-codimension bifurcations of the coupled oscillator systemare studied. Applying normal form theory and the centermanifold theorem, the stability and direction of the codi-mension bifurcations are determined. Finally, numericalresults are applied to illustrate the results obtained.

Jian PengHunan [email protected]

CP16

Effects of Degree-Frequency Correlations on Net-work Synchronization

We study network synchronization where internal dynam-ics (natural frequency) of each oscillator is correlated withlocal network properties (nodal degree). Recent studieshave found that such correlations can enhance synchro-nizability and cause explosive synchronization. Here weprovide a framework for studying the dynamics and de-scribe a class of correlations with remarkable dynamicalproperties. These results show that collective behavior innetwork-coupled dynamical systems can be made complexby creating correlations between dynamical and structuralproperties.

Per Sebastian SkardalDepartment of Applied MathematicsUniversity of Colorado at [email protected]

Jie SunClarkson [email protected]

Dane TaylorDepartment of Applied MathematicsUniversity of Colorado - Boulder

[email protected]

Juan G. RestrepoDepartment of Applied MathematicsUniversity of Colorado at [email protected]

CP16

Loop Searching System with Self-Recovery Prop-erty

We propose an autonomous system which is capable ofsearching for closed loops in a network in which nodes areconnected by unidirectional paths. A closed loop is definedas a phase synchronization of a group of oscillators belong-ing to the corresponding nodes. In addition, to develop asystem capable of self-recovery, we have developed novelregulatory rules for the interaction between nodes.

Kei-Ichi UedaRIMS, Kyoto [email protected]

CP17

Spectral Representation of Oscillators

Nonlinear flows exhibiting self-sustained oscillations arerepresented by the spectrum of the linear Koopman op-erator. The resonances (Koopman eigenvalues) given bythe trace of the Koopman operator form a lattice in thestable half of the complex plane. Near the critical param-eters for the onset of oscillations, the associated basis ofcoherent structures (Koopman modes) is constructed froma multiple-scale expansion of the flow field and a spectralexpansion of the corresponding amplitudes. Using the two-dimensional cylinder flow, it is shown that Ritz vectors andvalues extracted from the dynamic mode decomposition al-gorithm approximate the derived Koopman spectrum, aslong as the flow is on or near the limit cycle. Nonlinear dy-namics near the unstable equilibrium results in continuousdamped branches of Ritz values, that do not correspond toany discrete Koopman eigenvalues.

Shervin Bagheri

KTH Mechanics (Stockholm - Sweden)[email protected]

CP17

Building Energy Efficiency Using Koopman Oper-ator Methods

Building energy models have widespread use in evaluat-ing building performance. Models simulate thermal condi-tions at sub-hourly time-scales for the duration of a year.Despite their capability, zoning approximations, i.e., thesubdivision of building volume into regions with uniformproperties, is performed to manage complexity. By pro-jecting temperature histories of zones onto eigenmodes ofthe Koopman operator, a systematic approach to zoningis introduced. This technique is illustrated on a buildingmodel of an actual building.

Michael [email protected]

Igor MezicUniversity of California, Santa Barbara

112 DS13 Abstracts

[email protected]

CP17

Sparsity-Promoting Dynamic Mode Decomposi-tion

Dynamic mode decomposition (DMD) represents an effec-tive means for capturing the essential features of numeri-cally or experimentally generated flow fields. In order tostrike a balance between the quality of approximation (inthe least-squares sense) and the number of modes that areused to approximate the given fields, we develop a sparsity-promoting version of the standard DMD algorithm. Thisis achieved by combining tools and ideas from convex op-timization and the emerging area of compressive sensing.Several examples of flow fields resulting from simulationsand experiments are used to illustrate the effectiveness ofthe developed method.

Mihailo R. JovanovicElectrical and Computer EngineeringUniversity of [email protected]

Peter SchmidEcole Polytechnique Paris, FranceLaboratoire d’Hydrodynamique (LadHyX)[email protected]

Joseph W. NicholsCenter for Turbulence ResearchStanford [email protected]

CP17

Detecting Unstable Koopman Modes from PowerGrid Disturbance Data

Emergent disturbances in large-scale interconnected powergrids are repeatedly experienced in the world. We use theKoopman mode analysis based on the properties of thepoint spectrum of the Koopman operator for analysis ofdata on physical power flows sampled from a major distur-bance. This unveils the existence of unstable power flowpatterns that govern the complex dynamics occurring dur-ing the disturbance.

Yoshihiko SusukiKyoto UniversityDepartment of Electrical [email protected]

Igor MezicUniversity of California, Santa [email protected]

CP17

Comparison of PCA and Koopman Mode Decom-position Applied to Estuary Flow

We analyze near-bank velocities recorded by HADCP atWest Point NY in the Hudson River. To the north, a sharpbend and deep main channel disequilibrate flow during ebb(falling) tide, yielding an asymmetric temporal signature ofthe second PC. We want to characterize, then accuratelycompute, the dominant near-bank turbulent eddies. WithPCA and KMD, we aim to quantify spatiotemporal dynam-ics from field data, thence permitting rational comparison

with computation.

John WellsRitsumeikan [email protected]

Yoshihiko SusukiKyoto UniversityDepartment of Electrical [email protected]

Tuy N.M. Phan, Linh V. NguyenRitsumeikan Universitytuy [email protected], [email protected]

William Kirkey, Md. Shahidul Islam, James BonnerClarkson [email protected], [email protected],[email protected]

CP18

Energy-Level Cascades in Physical Scales of 3D In-compressible Magnetohydrodynamic Turbulence

Working in physical scales, total energy in 3D magnetohy-drodynamical turbulence is shown to cascade over an in-ertial range determined by a modified Taylor length scale.Direct cascades are investigated for energies transportedby distinct mechanisms. Also included are a comment onflux locality, a scenario in which the inter-medium energytransfer is predominantly kinetic to magnetic, and a noteregarding the cascade of kinetic energy for non-decayingfluid turbulence.

Zachary BradshawUniversity of [email protected]

Zoran GrujicDepartment of MathematicsUniversity of [email protected]

CP18

Analytical Approaches of One-Dimensional Con-servative Solute Transport in Hetrogeneous PorousMedium

To solves the analytically, conservative solute transportequation for a solute undergoing convection, dispersion,retardation in a one-dimensional inhomogeneous porousmedium. In the present study, the solute dispersion pa-rameter is considered uniform while the velocity of theflow is considered spatially dependent. Retardation factorand first order decay is also considered spatially dependent.The velocity of the flow is considered inversely proportionalto the spatially dependent function while retardation factorand first order decay is considered inversely proportionalto square of the velocity of flow. Analytical approachesintroduced for two cases: former one is for uniform in-put point source and latter case is for varying input pointsource where the solute transport is considered initiallysolute free from the domain. The variable coefficients inthe advection-diffusion equation are reduced into constantcoefficients with the help of the transformations which in-troduce by new space variables, respectively. The Laplacetransformation technique is used to get the analytical solu-tions. Figures are presented illustrating the dependence of

DS13 Abstracts 113

the solute transport upon velocity, dispersion and adsorp-tion coefficient.

Atul Kumar, R R YadavLucknow University, Lucknow, [email protected], yadav [email protected]

CP18

Deterministic Signature for Intermittent Convec-tive Transport in Turbulent Systems

In this letter we present evidences that intermittent trans-port observed in the scrape off layer of magnetically con-fined devices has a strong signature of determinism. Weshow that the universal distribution of density fluctuationas well as the unique parabolic relation between skewnessand kurtosis observed in experimental data can be ob-tained by a superposition of stochastic and deterministicevents. A well know deterministic effect, namely, the looseof transversal stability of periodic orbits embedded in aninvariant (inertial) manifold is used to model the spiky na-ture of the emissions. The intermittent emissions are pro-posed to be due to local unstable transversal directions ofthe invariant manifold resulting in an ejection of particlesand a consequent burst in the signal. We show that char-acteristics observed by the emissions namely an impulsiveejection followed by a slow recovery phase can be directlyrelated to the deterministic mechanism proposed.

Sergio R. Lopes, Paulo GaluzioDepartment of PhysicsFederal University of [email protected], [email protected]


Gustavo Limascience and technology schoolFederal University of Rio Grande do [email protected]

CP18

Inclination-Flip Homoclinic Orbits in AgeostrophicFlows with Viscoelastic-Type Reynolds Stress

An alternative title for this paper would perhaps be”Onset of Lorenz-type chaos in ageostrophic flows withviscoelastic-type Reynolds stress”. Although this paperis motivated by challenges in partial differential equations,our primary objective is to consider a two-mode Galerkinapproximation to ageostrophic flows with viscoelastic-typeReynolds stress given by the system of singularly perturbedordinary differential equations in R4:

RodX

dt= Y − EkX − λEkW,

dY

dt= rX − Y −XZ,

dZ

dt= −bZ +XY,

WedW

dt= ε(δλX −W ).

We note the foundation for the study of the low dimen-sional model, which capture the dominant energy bear-ing scales, from ageostrophic flows with viscoelastic-type

Reynolds stress, is the Lorenz equations modified throughsingular perturbation. Here, the variable X measures therate of convective overturning, the variable Y measures thehorizontal density variation, the variable Z measures thevertical density variation, and the variable W measures theReynolds stress. The parameter Ro is the Rossby number,Ek is the Ekman number, δ is the temporal shear-rate vis-cosity, r is proportional to the reciprocal of the Froudenumber, and We is the Weissenberg number. We continueour investigation to illustrate the existence of inclination-flip homoclinic orbits, via a bifurcation with a special typeof eigenvalue condition, taking account of degeneracies. Inorder to utilize geometric singular perturbation theory andMelnikov techniques, we perturb the problem and carrythe nonlinear analysis further to the question of the per-sistence of inclination-flip homoclinic orbits. This resultenables us to detect Lorenz-type chaos in singularly per-turbed dynamical systems. Open challenges are raised aswe celebrate the 50th anniversary of 1963 seminal papersby the troika of Lorenz, Melnikov and Smale.

Maleafisha Stephen TladiUniversity of Limpopo, South [email protected]

CP19

Chaos Induced Energy Hopping

A highly excited quasi one-dimensional Rydberg atom ex-posed to periodic alternating external electric ?eld pulsesexhibits chaotic behavior. Time evolution of this systemis governed by a geometric structure of phase space calleda homoclinic tangle and its turnstile. We use the knowl-edge about the geometric structure of phase space to designshort pulse sequences that quickly and efficiently transferelectronic wave packet from an initial state (n 306) to ei-ther a much lower energy state (n 150) or a much higherenergy state (n 500). We present how the phase space ge-ometry influences the efficiency of the transport betweenthe energy states.

Korana BurkeUC [email protected]

Kevin A. MitchellUniv of California, MercedSchool of Natural [email protected]

Shuzhen Ye, Barry DunningRice [email protected], [email protected]

CP19

Nonlinear Dynamics of Photoinduced StructuralChange in Molecular Crystals

We discuss the nucleation dynamics of photoinduced struc-tural change by a model of molecular crystals. The nona-diabaticity of electron dynamics is fully taken into accountby quantizing the relevant phonon modes, and the spa-tiotemporal patterns of photoinduced domains are studiedby methods of non-equilibrium statistical mechanics andmultifractal analysis. We found that the formation of aprecursor state of photoinduced nuclei in ultrashort timescale causes the nonlinearity of the nucleation dynamics.

Kunio Ishida

114 DS13 Abstracts

Corporate Research and Development CenterToshiba [email protected]

Keiichiro NasuInstitute of Materials Structure [email protected]

CP19

Modeling Temperature Dynamics of InductivelyHeated Shape Memory Polymers Doped with Mag-netic Nanoparticles

Various methods have been considered for heating shapememory polymers when noncontact heating is required,including inductive heating. However, nonlinear thermaldynamics and the hysteresis present significant challengesin modeling the dynamics. The purpose of this researchis to develop a model for inductively heated polymersdoped with magnetic nanoparticles. We discuss the well–posedness of the time discretized model and a comparisonof the numerical results with experimental data in existingliterature.

Peter Kay, Dinesh EkanayakeWestern Illinois [email protected], [email protected]

CP19

Reduced Order Modeling of a Nonlinear Piezoelec-tric Energy Harvester

An infinite dimensional model has been developed for abistable asymmetric broadband energy harvesting deviceconsisting of piezoelectric beams in a buckled configura-tion. To aid in qualitative understanding of the behavior ofthis device, Galerkin projection onto analytic mode shapeshas been used to reduce the order of this model. We re-view the reduced order model and compare to experimentalresults to confirm validity.

Louis Van BlariganUniversity of California Santa [email protected]


CP20

The Sigma-Delta Modulator as a Chaotic Nonlin-ear Dynamical System

Sigma-Delta modulators are extensively used for ana-logue/digital signal processing. I explore their chaotic be-haviour from the point of view of nonlinear dynamical sys-tems analysis. I conduct a theoretical study of conditionsfor chaos using an adaptation of Devaney’s definition ofchaos. I then introduce a stochastic formulation of thelong-run dynamics, which is applied to give conditions foruniformly distributed error behaviour (relevant to ditheredcontrol of error statistics).

Donald O. CampbellUniversity of [email protected]

CP20

Families of Hyperbolic Lorenz Knots

We have defined families of hyperbolic Lorenz knots basedon the Birman and Kofman lists which we conjecture to behyperbolic, supported on extensive computational testing.We have also interpreted El-Rifai’s satellite knots construc-tions in terms of Lorenz braids, Lorenz vectors and sym-bolic sequences, obtaining algorithms for this operation.This, along with previous work, allows us to compute sev-eral Lorenz knots invariants, and also to test if a givenLorenz knot is a satellite knot.

Nuno FrancoCIMA-UE andDepartment of Mathematics, Evora University, [email protected]

Luis F. SilvaDepartmental Area of Mathematics,ISEL-Lisbon Superior Engineering [email protected]

Gomes PauloDepartment of Mathematics,ISEL/ Lisbon Superior Institute of [email protected]

CP20

On the Chaotic Cubic-Quintic Oscillator

In this paper, we used Hamiltonian formulation and Lietransform to investigate cubic-quintic nonlinear oscillator.Using Chirikov’s overlap criterion we find the critical value,at which the chaos loses its local character and becomesglobal. The results of Lie transformation analysis andChirikov’s criteria for the oscillator are compared with nu-merically generated Poincare Maps.

Patanjali SharmaDepartment of Mathematics and Statistics,Banasthali University, Banasthali, INDIA [email protected]

CP20

Invariants of Templates, Knots and Links Gener-ated by Renormalizable Lorenz Maps

We describe the sub-Lorenz templates generated by renor-malizable Lorenz maps, in terms of the templates generatedby the renormalized map and by the map that determinesthe renormalization type. Consequently we obtain explicitformulas for the Williams ζ function of renormalizable sub-Lorenz templates and also for the genus and the braid indexof renormalizable Lorenz knots and links.

Luis F. SilvaDepartmental Area of Mathematics,ISEL-Lisbon Superior Engineering [email protected]

CP20

Almost Lyapunov Functions

A well-known method for showing convergence of all so-lutions of an ODE x = f(x) to an equilibrium consists infinding a Lyapunov function V (x) which is a positive (awayfrom the equilibrium) smooth function that decays along

DS13 Abstracts 115

all non-zero solutions V ′(x) ·f(x) < 0. Suppose now that acandidate Lyapunov function decays everywhere except fora set of small measure. Given the measure of the “bad’ set,this work gives necessary conditions on f(x), V (x) whichstill assure some type of stability.

Vadim ZharnitskyDepartment of MathematicsUniversity of [email protected]

Daniel LiberzonDepartment of Electrical and Computer EngineeringUniversity of [email protected]

Charles YingDepartment of Electrical and Computer EngineeringUniversity of [email protected]

CP21

Synaptic Architecture that Promotes Robust Spa-tiotemporal Neural Dynamics

Spatial models of neuronal networks often assume thatsynaptic connectivity depends only on the distance be-tween neurons. Such dynamical systems are marginallystable, so solutions diffuse in the presence of noise. Morerealistic models of neuronal connectivity include spatialheterogeneity. The resulting systems do not exhibit de-generacies such as translation invariance. In this talk, wewill explore how breaking the symmetry of spatial con-nectivity in models of neuronal networks can make theirdynamics more robust. Specifically, we focus on how wellbumps stay in the vicinity of their initial position in thepresence of noise.

Zachary KilpatrickUniversity of [email protected]

CP21

Formation and Maintenance of Multistability inBalanced Neuronal Networks with Plasticity

Neuronal networks in cortex exhibit complex and vari-able patterns of activity even in the absence of a stim-ulus. These dynamics may reflect fluctuations betweendifferent stable attractor states. However, attractor net-works require specific connectivity patterns to ensure ex-citation and inhibition remain in balance while preservingmultistability. We investigate how this connectivity maybe maintained. We show that simple homeostatic plastic-ity rules that regulate excitatory and inhibitory synapticstrengths can lead to robust multistability in balanced net-works without fine-tuning of parameters. These rules en-sure that the system stochastically samples its full reper-toire of attractor states, leading to rich spontaneous dy-namics.

Ashok Litwin-KumarCarnegie Mellon [email protected]

CP21

Heterogeneity-induced Transitions in Large-scale

Systems

I will present derivation and analysis of mean-field equa-tions in the presence of heterogeneities i) in the synapticconnections and ii) in the transmission delays (related tothe distances between neurons). The dynamics of the limitequation will evidence a number of phase transitions be-tween stationary and periodic solutions as a function ofthe degree of heterogeneity, related in the case of hetero-geneous delays to the topology of the cortical area.

Jonathan D. TouboulThe Mathematical Neuroscience LaboratoryCollege de France & INRIA [email protected]

CP21

Complexity of Random Neural Networks

We investigate the explosion of complexity arising near thephase transition to chaos in random neural networks. Weshow that the mean number of equilibria undergoes a sharptransition from one equilibrium to a very large number scal-ing exponentially with the dimension on the system. Nearcriticality, we compute the exponential rate of divergence,called topological complexity. Strikingly, we show that itbehaves exactly as the maximal Lyapunov exponent, sug-gesting a deep and underexplored link between topologicaland dynamical complexity.

Gilles WainribUniversite Paris [email protected]

CP22

Accuracy and Stability of the Continuous-Time3dvar-Filter for 2D Navier-Stokes Equation

We consider a noisy observer for an unknown solution ofa deterministic model. The observer is a stochastic modelarising in the limit of frequent observations in filtering,where noisy observations of the low Fourier modes togetherwith knowledge of the deterministic model are used to trackthe unknown solution. We establish stability and accuracyof the filter by studying this for the stochastic PDE de-scribing the observer.


Kody LawUniversity of [email protected]

Andrew StuartMathematics Institute,University of [email protected]

Konstantinos ZygalakisUniversity of [email protected]

CP22

The Numerical Integration of a Convection Prob-lem with Temperature Dependent Viscosity: Sim-

116 DS13 Abstracts

ulations and Results

We propose spectral numerical methods to solve the timeevolution of a convection problem in a 2D domain withviscosity strongly dependent on temperature. At a fixedaspect ratio the analysis is assisted by bifurcation tech-niques such as branch continuation. Stable stationary so-lutions become unstable through a Hopf bifurcation afterwhich the time dependent regime is solved by the spectraltechniques. We discuss some results on how different vis-cosity laws affect the formation and morphology of thermalplumes.

Jezabel Curbelo, Ana M. ManchoInstituto de Ciencias [email protected], [email protected]

CP22

Navier-Stokes Equations on Rotating Surfaces:Regularity, Algorithm, Analysis, Simulations

Development of efficient algorithms with rigorous analy-sis for partial differential equations (PDE) on domains andsurfaces requires knowledge of the regularity of solutions ofthe PDE. In this talk, for the Navier-Stokes equations onrotating spheres we discuss (i) the global regularity for realand complexified time; (ii) a high-order algorithm with sta-bility and convergence analysis; (iii) long time simulationof a benchmark atmospheric flow model and justificationof a turbulence theory.

Mahadevan GaneshColorado School of [email protected]

CP22

Study of Explicit and Implicit Time IntegrationMethods for Various Low Mach Number Precon-ditioners and Low Dissipation Schemes Applied toSteady and Unsteady Inviscid Flows

The performance of many existing compressible codes de-grades as the Mach number of the flow tends to zero andleads to inaccurate computed results. To alleviate theproblem, Roe-type based schemes have been developed forall speed flows, such as the preconditioned Roe and lowdissipation schemes. To solve this preconditioned equa-tions for steady and unsteady state solution, there existmany explicit and implicit time integration strategies. Forexplicit steady formulation Euler, classical RK4 and 5-stage Martinelli-Jameson(MJ) time integration techniquesare considered, while for implicit backward Euler with fluxlinearization method is studied. In unsteady state sim-ulation, Dual-time stepping formulation is used. For ex-plicit unsteady state formulation Euler(τ )-BDF2(t), classi-cal RK4 and 5-stage MJ with Euler(τ )-BDF2(t) discretiza-tion are considered, while for implicit physical time is dis-cretized using backward Euler and BDF2 scheme with fluxlinearization are studied.

Ashish GuptaUniversity of Tennessee at [email protected]

CP22

An Online Manifold Learning Approach for ModelReduction

An online manifold learning method is developed for di-

mensional reduction of dynamical systems. The methodmay be viewed as a variant of Picard iteration combinedwith a model reduction procedure. Specifically, startingwith a test solution, we solve a reduced model to obtaina better approximation, and repeat this process until suf-ficient accuracy is achieved. Convergence of the proposedmethod is proved. The accuracy of the proposed methodis demonstrated by Navier-Stokes equation.

Liqian PengUniversity of [email protected]

Kamran MohseniUniversity of Florida, Gainesville, [email protected]

CP23

Phase Characterization of Complex Systems

In this work we present a new approach for measuring thephase of complex systems. The approach is based on find-ing sinusoidal fits to segments of the signal therefore ob-taining, for each segment, an appropriate frequency fromwhich a phase can be derived. The method is adjustableto different types of signals and robust against moderatenoise levels. Three cases are presented for demonstratingthe applicability of the method.

Rosangela FollmannPolytechnic School of University of Sao [email protected]

Elbert E. MacauINPE - Brazilian National Institute for Space ResearchLAC - Laboratory for Computing and [email protected]


Jose Roberto Castilho PiqueiraPolytechnic School of University of Sao [email protected]

CP23

Gyrostatic Extensions of the Lorenz 1963 Systemas Novel Time Series Models for Atmospheric Data

The talk will discuss the authors finite systems of ODEsin the form of coupled Volterra gyrostats (gyrostatic mod-els, the simplest being equivalent to the Lorenz system)developed for modeling atmospheric flows. Due to recentprogress in understanding statistical properties of dynam-ical systems, exemplified by results for the Lorenz system,gyrostatic models may provide a viable alternative to thoseborrowed from standard time series analysis, which involvestrong assumptions rarely met in real data.

Alexander GluhovskyPurdue [email protected]

CP23

Stability of Intrinsic Localized Modes in Paramet-

DS13 Abstracts 117

rically Driven Coupled Cantilever Arrays

A micro-cantilever array can be modeled as the nonlinearcoupled oscillator in which quartic nonlinearity appear inboth on-site and inter-site potentials. It is known that thestability of intrinsic localized mode (ILM) is flipped whenthe ratio between the on-site and the inter-site nonlineari-ties. In this poster, the stability of ILM will numerically bediscussed for the system in which the ratio is sinusoidallyvaried in time, namely the parametrically driven system.

Masayuki KimuraSchool of EngineeringThe University of Shiga [email protected]

Takashi HikiharaDepartment of Electrical EngineeringKyoto [email protected]

Yasuo MatsushitaSchool of EngineeringThe University of Shiga [email protected]

CP23

Challenges and Tools for State and Parameter Es-timation from Time Series

Which model fits best to my data? Which parametersof the model of interest can be (reliably) estimated fromobservations? Has the identified model predictive power?Can the observed dynamics (approximately) be describedby a “simple’ (low-dimensional) mathematical model? Toaddress these questions we shall use coarse grained descrip-tions of the dynamics in terms of ordinal patterns, non-linear dimension reduction methods, optimization basedestimation methods, automatic differentiation, and a sen-sitivity analysis based on delay embedding of time series.All relevant tasks, major obstacles, and suggested solu-tions will be illustrated using chaotic dynamical systems in-cluding (spatially-extended) high-dimensional models fromphysics and biology (e.g. cardiac cells).

Ulrich ParlitzUniversity of [email protected]

Jan Schumann-Bischoff, Stefan LutherMax Planck Institute for Dynamics and [email protected],[email protected]

CP24

Connecting Curves in Higher Dimensions

Chaotic attractors can exhibit large-scale bifurcations astheir control parameters are varied. In higher dimensions,these bifurcations result in structural changes that can beunderstood in terms of vortices, hyper-vortices and the vor-tex core lines that identify them in phase space. We usecuspoid catastrophes An, n=3,4,5, to describe the struc-tural changes that can occur in a class of n-dimensionaldifferential dynamical systems.

Greg ByrneGeorge Mason [email protected]

Bob GilmoreDrexel Universityn/a

CP24

Explicit Inhomogeneities in Symmetry-BreakingSystems

Equivariant theory can be used to analyze pattern formingsystems, and has been extended to encompass systems withexplicit anisotropies. We use group theory to examine gen-eral (i.e., model-independent) pattern formation with anexplicitly inhomogeneous background, such as for a Turinginstability occuring on a periodic substrate. The presenceof such inhomogeneities can create new solutions and dy-namics.

Timothy K. CallahanArizona State UniversityDepartment of Mathematics and [email protected]

CP24

Mathematical Physics of Cellular Automata

A universal map is presented valid for all deterministic 1Dcellular automata (CA). It can be extended to an arbitrarynumber of dimensions and topologies and its invariances al-low to classify all CA rules into equivalence classes. Com-plexity in 1D systems is then shown to emerge from theweak symmetry breaking of the addition modulo an inte-ger number p. The latter symmetry is possessed by certainrules that produce Pascal simplices in their time evolution.

Vladimir Garcia-MoralesInstitute for Advanced StudyTechnische Universitat [email protected]

CP24

Unfolding the Piecewise Linear Analogous of Hopf-Zero Bifurcation

Three-dimensional symmetric piecewise linear differentialsystems near the conditions corresponding to the Hopf-zero bifurcation for smooth systems are considered. Byintroducing one small parameter, we study the bifurcationof limit cycles in passing through its critical value, whenthe three eigenvalues of the linear part at the origin crossthe imaginary axis of the complex plane. The simultaneousbifurcation of three limit cycles is proved. Conditions forstability of these limit cycles are provided, and analyticalexpressions for their period and amplitude are obtained. Ageneralized version of Chua’s circuit is shown to undergosuch Hopf-zero bifurcation for a certain range of parame-ters.

Enrique PonceDepartamento de Matematica AplicadaEscuela Tecnica Superior de Ingenieros, Seville, [email protected]

Javier Ros, Elisabet VelaUniversidad de [email protected], [email protected]

118 DS13 Abstracts

CP24

Morse Theory for Lagrange Multipliers

Given f, μ : Rn → R, one studies critical points off |μ−1(0) using the Lagrange multiplier function F : R\ ×R → R, F(§, η) = {(§) + ημ(§). The gradient flow of F ,after rescaling the metric on R by λ−2, is

x′ = − (∇f(x) + η∇μ(x)) , η′ = −λ2μ(x).

The homology of the Morse-Smale-Whitten complex of Fis independent of λ. We show that in the limit λ → ∞ weobtain the complex for f |μ−1(0), and in the limit λ → 0we obtain a complex whose homology can be computedusing geometric singular perturbation theory.

Stephen SchecterNorth Carolina State UniversityDepartment of [email protected]

Guangbo XuPrinceton [email protected]

CP25

Existence and Stability of Left-Handedness: AnEvolutionary Model

An overwhelming majority of humans are right-handed.I will present a novel mathematical model and use it totest the idea that population-level hand preference rep-resents a balance between selective costs and benefits inhuman evolutionary history. Supporting evidence comesfrom handedness distributions among elite athletes; ourmodel can quantitatively account for these distributionswithin and across many professional sports. The modelcan also explain the absence of consistent population-level“pawedness’ in many animal species.

Daniel AbramsNorthwestern [email protected]

Mark J. PanaggioEngineering Science and Applied MathematicsNorthwestern [email protected]

CP25

Ecological and Evolutionary Stability of Single-Species Dispersal in a Two-Patch Habitat

Natural selection is an evolutionary mechanism thatstrongly affects species diversity. At suitable spatial scales,landscapes are not heterogeneous. To begin to answer howmovement strategies might evolve, we analyze a simplesingle-species ordinary differential equation model describ-ing theoretical movement between two different habitats.Combining analytical and numerical methods, we identifyevolutionarily singular dispersal strategies, show that theyare evolutionarily and convergence stable, and describehow two different types of costs affect these strategies.

Theodore E. GalanthayUniversity of [email protected]

CP25

Alternate Models of Replicator Dynamics

This work concerns models of evolutionary dynamics,which combine differential equations with game theory. Inparticular, we study systems of the form xi = g(xi)(fi−φ),called replicator dynamics, in the context of rock-paper-scissors (RPS) games. Here g is a natural growth function;fi = (Ax)i is the fitness of strategy i, where A is the RPSpayoff matrix; and φ =

∑ig(xi)fi/

∑ig(xi) is the average

fitness. The standard replicator equation takes g(xi) = xi.We analyze the case g(xi) = xi−αx2

i , which exhibits richerdynamics.

Elizabeth N. WessonCornell [email protected]

Richard H. RandCornell UniversityDept of Theoretic & Appl [email protected]

CP26

Competitive Modes As Reliable Predictors ofChaos Versus Hyperchaos, and As Geometric Map-pings Accurately Delimiting Attractors

We consider real quadratic dynamics in the context of com-petitive modes. We consider hyperchaotic systems, andconclude that they exhibit three competitive modes, in-stead of two as for chaotic systems . And, in a novel twist,we re-interpret the components of the Competitive Modesanalysis as simple geometric criteria to map out the spatiallocation and extent, as well as the rough general shape, ofthe system attractor for any parameter sets correspondingto chaos.

Roy ChoudhuryUniversity of Central [email protected]

Robert Van GorderDepartment of MathematicsUnversity of Central [email protected]

CP26

Integrated Semigroups and the Cauchy Problemfor Some Nonelinear Fractional Differential Equa-tions

Let A be a linear closed operator defined on a dense set ina Banach space E to E. In this note it is supposed that Ais the generator of α - times integrated semigroup, where αis a positive number. The abstract Cauch problem of thefractional abstract differential equation:

dβu(t)

dtβ= Au(t) + f(t, u),

with the initial condition: u(0) = u0 ∈ E, is studied,where 0 < β ≤ 1, and f , is a given nonelinear abstractfunction. The solution of the Cauchy problem is obtainedunder suitable conditions on f . An application is given.

Mahmoud M. El-BoraiProf.of Math. Dep. of Mathematics Faculty of ScienceAlexandria University Alexandria Egyptm m [email protected]

DS13 Abstracts 119

CP26

Classifying Workload Using Discrete DeterministicNonlinear Models

We illustrate the use of a novel deterministically chaoticclassification algorithm. The algorithm is used to classifyhuman subject cognitive workload using only the subjectselectrocardiogram (ECG) as input. Presented are the al-gorithm and a case study, in which the algorithm is used todiscretely classify the level of a subjects cognitive workloadfor various tasks. Presentation is given to the accuracy ofthe chaotic classifier for the domain of cognitive workloadusing surrogate tasks.

Joseph Engler, Thomas SchnellOperator Performance LaboratoryUniversity of [email protected], [email protected]

CP26

Finite-Time Lyapunov Analysis of Two TimescaleSystems

Finite-time Lyapunov exponents and vectors are used todefine and diagnose boundary-layer type, two-timescale be-havior in finite-dimensional nonlinear systems and to de-termine an associated slow manifold when one exists. Two-timescale behavior is characterized by a slow-fast splittingof the tangent bundle for a not necessarily invariant statespace region. Invariance-based orthogonality conditionsare used to identify the associated manifold structure.

Kenneth MeaseUniversity of California, [email protected]

Marco MaggiaUniversity of California [email protected]

CP26

The Memory of Non-Smooth Systems

Traditional mode decomposition techniques are inaccuratefor impacting systems. The effect of the impact is of thesame order for all modes, therefore increasing the num-ber of modes leads to a diverging description. Here, Iwill introduce a method that decouples the impact fromthe infinitely many modes by transforming the system intoan equivalent low-dimensional delay equation. Within thisframework I obtain a converging description as the delayterms are independent of the impact.

Robert SzalaiUniversity of [email protected]

CP27

Parametrically Driven Oscillators with AddedNoise

A theoretical model that describes the dynamics of para-metrically driven oscillators with added thermal noise isreported here. Quantitative estimates for heating andquadrature thermal noise squeezing near the threshold tothe first parametric instability are given [1]. Further-more, we describe parametric amplification, which is ex-tremely selective in frequency and phase of the exter-

nal signal, and presents a high output signal-to-noise ra-tio [2].$[1]A.A.Batista, Phys.Rev.E86, 051107(2012).$[2]A.A. Batista and R. S. N. Moreira, Phys. Rev. E 84,061121 (2011).

Adriano A. BatistaDepartment of PhysicsUniversity of [email protected]

CP27

Nondeterminism of Piecewise Smooth System

A close look at the dynamics of piecewise smooth systemsreveals that their peculiarity goes way beyond nondifferen-tiable orbits and sliding regions. Lack of smoothness entailsloss of uniqueness of solutions both forward and backwardin time, and a consequential loss of determinism. I will dis-cuss some of these exotic behaviours and their relation tothe real-world phenomena that they attempt to describe.

Alessandro ColomboMassachusetts Institute of [email protected]

CP27

Conditionally Stationary Measures for RandomDiffeomorphisms

For random diffeomorphisms the relations between condi-tionally stationary measures and controllability propertiesof an associated deterministic control system are investi-gated. The main result gives conditions implying that thesupport of such a measure is the closure of a relatively in-variant control set. This result generalizes known resultscharacterizing the supports of stationary measures by in-variant control sets. This paper may be viewed as a contri-bution of open dynamical systems, here for random systemsand control systems.

Fritz ColoniusUniversity of [email protected]

CP27

Modelling Computer Dynamics: Can ComplexityOvershadow Determinism?

To predict computer performance, one needs effective andinformative models of computer dynamics. Traditional ap-proaches to this employ linear stochastic methods; newwork suggests that nonlinear deterministic methods aremore appropriate. It turns out that neither approach issuccessful in all cases, which raises a larger research ques-tion: given a time series from an arbitrary dynamical sys-tem, how can one decide which modelling strategy willwork better? We will propose information-theoretic met-rics for this task.

Joshua GarlandUniversity of Colorado at [email protected]

Elizabeth BradleyUniversity of ColoradoDepartment of Computer [email protected]

120 DS13 Abstracts

CP27

Dynamical Regimes and Transitions in Plio-Pleistocene Asian Monsoon

We propose a novel approach based on the fluctuation ofsimilarity to identify regimes of distinct dynamical com-plexity in short time series. A statistical test is devel-oped to estimate the significance of the identified transi-tions. Our method is verified by uncovering bifurcationstructures in several paradigmatic models, providing morecomplex transitions compared with traditional Lyapunovexponents. In a real-world situation, we apply this methodto identify millennial-scale dynamical transitions in Plio-Pleistocene proxy records of the South Asian summer mon-soon system. We infer that many of these transitions areinduced by the external forcing of the solar insolation andare also affected by internal forcing on Monsoonal dynam-ics, i.e., the glaciation cycles of the Northern Hemisphereand the onset of the Walker circulation.

Nishant MalikDepartment of MathematicsUniversity of North Carolina at Chapel [email protected]

Yong ZouDepartment of Electronic and Information EngineeringThe Hong Kong Polytechnic University Hung Hom,Kowloon, [email protected]

Norbert MarwanPotsdam Institute for Climate Impact [email protected]


CP28

The Rhomboidal Symmetric Mass Four-BodyProblem

We consider the existence and stability of periodic solutionswith regularizable collisions in the rhomboidal symmetric-mass four-body problem. In two degrees of freedom, wherethe analytic existence of the periodic solutions is given by avariational method, the periodic solutions are numericallylinearly stable for most of the values of the mass parameter.In four degrees of freedom, we establish the analytic exis-tence of the periodic solutions and numerically investigatetheir linear stability.

Lennard F. Bakker, Skyler SimmonsBrigham Young [email protected], skyler simmons¡[email protected]¿

CP28

Integrable Many-Body Models on a Circle

We use generalized Lagrangian interpolation and finite-dimensional representations of differential operators to con-struct various many-body models, which describe N pointsconfined to move on a plane circle. Their Newtonian equa-tions of motion are integrable, i. e. they allow the ex-plicit exhibition of N constants of motion in terms of the

dependent variables and their time-derivatives. Some ofthese models are moreover solvable by purely algebraicoperations, by (explicitly performable) quadratures and,finally, by functional inversions. This is a joint workwith Francesco Calogero from the University of Rome ”LaSapienza”.

Oksana BihunConcordia College, Moorhead, [email protected]

CP28

Collinear Equilibrium Points and Linear Stabilityin the Generalized Photogravitational Chermnykh-Like Problem with Power-Law Profile

We have considered the motion of infinitesimal mass inthe generalized photogravitational Chermnykh-like prob-lem with power-law profile. The collinear equilibriumpoints of the proposed problem are determined. In additionwith three, a new collinear equilibrium point is obtained.Again, we have examined linear stability of the points andnoticed that generally, all the collinear points are unstablebut some are stable for specific values of inner and outerradii of the disk.

Ram Kishor, Badam Singh KushvahIndian School of Mines, Dhanbad-826004,Jharkhand, [email protected], [email protected]

CP28

Stability of Relative Equilibria in the N-VortexProblem

In the weather research and forecasting models of certainhurricanes, “vortex crystals’ are found within a polygonal-shaped eyewall. These special configurations can be inter-preted as relative equilibria (rigidly rotating solutions) ofthe point vortex problem introduced by Helmholtz. Theirstability is thus of considerable importance. Adapting anapproach of Moeckel’s for the companion problem in celes-tial mechanics, we present some useful theory for study-ing the linear stability of relative equilibria in the planarN-vortex problem. For example, we show that when thevorticities are all of the same sign, a relative equilibrium islinearly stable if and only if it is a minimum of the Hamilto-nian restricted to a level surface of the moment of inertia.Some symmetric examples will be presented, including alinearly stable family of rhombi in the four-vortex prob-lem.

Gareth E. RobertsDept. of Mathematics and C.S.College of the Holy [email protected]

CP28

Implementation of Dynamical Systems Techniquesfor the Mars-Phobos Three-Body Problem withAdditional Gravity Harmonics

Following ESAs proposal for a sample-return mission toPhobos, this paper analyses the orbital dynamics of theMars-Phobos system to provide low-cost observation pointsfor exploration. The proposed nonlinear model of a space-crafts motion in the vicinity of Phobos incorporates thehighly inhomogeneous gravity field into a restricted three-body problem. State-of-the-art analytical and numerical

DS13 Abstracts 121

methodologies from dynamical systems theory are used toidentify periodic orbits around the libration points.

Mattia ZamaroAdvanced Space Concepts [email protected]

James BiggsUniversity of [email protected]

CP29

Intra-Community Clustering and Solvency in aSimulated Banking Network Model

We present a model of a banking network where connectiv-ity occurs in the form of simulated 3-day interbank loansoccurs based on two selection models. Average system sol-vency is assessed in the context of community average be-tweeness centrality for each of 300 banks. Results showthat while fundamental clustering characteristics do notchange between the two selection methods, system solvencyis impacted by the method used to select overnight lenders.

Peter C. AnselmoNew Mexico Institute of Mining and [email protected]

CP29

Twitter Reciprocal Reply Networks Exhibit Assor-tativity with Respect to Happiness

The advent of social media has provided an extraordinary,if imperfect, big data window into the form and evolution ofsocial networks. Based on nearly 40 million message pairsposted to Twitter between September 2008 and February2009, we construct and examine the revealed social networkstructure and dynamics over the time scales of days, weeks,and months. At the level of user behavior, we employ ourrecently developed hedonometric analysis methods to in-vestigate patterns of sentiment expression. We find usersaverage happiness scores to be positively and significantlycorrelated with those of users one, two, and three linksaway. We strengthen our analysis by proposing and usinga null model to test the effect of network topology on theassortativity of happiness. We also find evidence that morewell connected users write happier status updates, with atransition occurring around Dunbar’s number. More gen-erally, our work provides evidence of a social sub-networkstructure within Twitter and raises several methodologicalpoints of interest with regard to social network reconstruc-tions.

Catherine A. BlissUniversity of VermontDepartment of Mathematics and [email protected]

Isabel KloumannDepartment of MathematicsCornell [email protected]

Kameron D. HarrisUniversity of [email protected]

Chris Danforth

Mathematics and StatisticsUniversity of [email protected]

Peter DoddsUniversity of [email protected]

CP29

Time-Scale Lyapunov Functions for Incentive Dy-namics on Riemannian Geometries

Time-scale calculus allows the study of difference and dif-ferential equations simultaneously. In this talk we presentthe application of time-scale Lyapunov stability theory togame-theoretically inspired incentive dynamics on the sim-plex for a wide class of Riemannian geometries, giving time-scale Lyapunov functions in terms of information diver-gences for a large class of discrete and continuous-time dy-namics that include many well-known dynamical systemsin evolutionary game theory. These results include discretetime extensions of the adaptive dynamics of Hofbauer andSigmund. We also discuss the relationship between incen-tive stability and evolutionary stability through a series ofillustrative examples.

Dashiell FryerDeparment of MathematicsPomona [email protected]

Marc [email protected]

CP29

Fractal Encoding of Recursive Dynamics

Under a standard model of human language, recursivestructures are encoded as complex constellations of inter-dependent rules. One wonders how children learn suchconstellations because every part needs to be in place forthe system to function at all. Neural network dynamicalsystems solve the all-at-once problem by adopting fractalencodings, which grow continuously from simple sets. Weexamine conditions under which the learning is robust inthe presence of neural and sequence noise.

Whitney TaborUniversity of [email protected]

Harry DankowiczUniversity of Illinois at Urbana-ChampaignDepartment of Mechanical Science and [email protected]

Pyeong Whan Cho, Emily SzkudlarekUniversity of [email protected], [email protected]

CP29

Optimal Control of the Spread of Marijuana Smok-ing Among the Youth

Reducing the number of individuals involved in substanceabuse in any community is usually a challeging problem.We consider the control of the spread of Marijuana smok-

122 DS13 Abstracts

ing, one substance that is majorly abused, among theyouth. We propose a deterministic model for con- trollingthe spread of Marijuana smoking incorporating educationand awareness campaign as well as rehabilitation as con-trol measures. We formulate a fixed time optimal controlproblem subject to the model dynamics with the goal offinding the optimal combination of the control measuresthat will minimize the cost of the control efforts as well asthe prevalence of marijauna smoking in a community. Weuse Pon- tryagin’s maximum principle to derive the opti-mality system and solve the system numerically. Resultsfrom our simulations are discussed.

Tunde Tajudeen YusufFederal University of Technology AkureOndo [email protected]

Olubode Kolade KorikoDept. of Maths Sciences, Fed. Univ. of TechnologyAkure,Ondo state, [email protected]

CP30

Topological Structures and Parameter-SweepingTechniques in the Hindmarsh-Rose Neuron Model

The use of computer techniques permits to help the under-standing of natural phenomena. Among the mathemati-cal models of neuronal activity, the Hindmarsh and Rosemodel is one of the most used in simulations. In this talkwe show the use of new techniques based on neurocomput-ing parameters to study the global behaviour of the systemand we link them with bifurcation techniques. Moreover westudy the structure of the chaotic attractors that may ap-pear when the parameters are changed, providing us withtopological templates which “quantify” the differences andsimilarities between the structures observed.

Roberto BarrioUniversity of Zaragoza, [email protected]

Marc LefrancPhLAM/Universite Lille I,[email protected]

M. Angeles MartinezUniversity of [email protected]

Sergio SerranoUniversity of Zaragoza, [email protected]

Andrey ShilnikovNeuroscience Institute and Department of MathematicsGeorgia State [email protected]

CP30

Singularity Theory Sheds Light on Bursting Mech-anisms in Conductance-Based Models

In recent work, we have shown that a pitchfork bifurcation

organizes the excitability of arbitrary conductance-basedmodels. Here we study a two-dimensional universal unfold-ing of this bifurcation augmented with a slow adaptationvariable. The resulting three-dimensional dynamics pro-vide a minimal model of bursting as paths in the universalunfolding of the pitchfork. We discuss the generality of thisapproach and argue that it provides a physiological routeto neuronal bursting.

Alessio FranciUniversity of [email protected]

Guillaume DrionNeurophysiology Unit and GIGA NeurosciencesUniversity of Liege, Liege, [email protected]

Rodolphe SepulchreUniversity of [email protected]

CP30

Minimum Energy Control for in Vitro Neurons

The applicability of control theory in regulating the inter-spike interval for single periodically-firing in vitro neu-rons is demonstrated. Combining electrophysiology experi-ments with optimal control theory, first the phase responsecurve for each neuron is measured, then continuous-time,charge-balanced, minimum energy control waveforms aredesigned that optimally change the next spike time for theneuron with significantly lower levels of energy comparedto those of previous approaches.

Ali NabiUC Santa [email protected]

Tyler StigenDept. of Biomedical Eng.U. [email protected]


Theoden I. NetoffUniversity of MinnesotaDepartment of Biomedical [email protected]

CP30

Singularly Perturbed Phase Response Curves

Motivated by models of spiking neurons, we determine theshape of (non-infinitesimal) phase response curves for slow-fast systems from the singular limit. It is completely deter-mined by the bistable range of the fast subsystem and thebifurcations that delineate its onset and its termination.We apply this geometric approach to relaxation oscillatorsand bursters, recovering among others the fast thresholdmodulation phenomenon.

Pierre Sacre

DS13 Abstracts 123

Universite de [email protected]

Alessio FranciUniversity of [email protected]


CP30

Global Sensitivity of Spiking Neuron Models: ThePower of a Local Analysis

This study focuses on two important sensitivity measuresfor reliable transmission of information in single neuronmodels: the variability of the first spike latency and theprobability of doublets. Our analysis, supported by singu-lar perturbation theory, shows that these two global sensi-tivity measures can be characterized locally, in the vicin-ity of local bifurcations. Results are illustrated on severalconductance-based models of spiking neurons.

Laura Trotta, Alessio FranciUniversity of [email protected], [email protected]


CP31

Network Topological Conditions for StochasticallyAmplified and Coherent Oscillations

We investigate relationship between stochastic oscillationsand topologies of biochemical reaction networks. We con-sider all topologies of three-nodes biochemical reaction net-works with mass-action kinetics and characterize noisy os-cillatory behaviors by using linear noise approximation ofthe corresponding master equations. All networks withboth negative and positive feedbacks are deterministicallystable, but capable to generate stochastically amplifiedand coherent oscillations. We use stochastic center mani-fold reduction to demonstrate that various network topolo-gies that exhibit the same stochastic oscillations could bemapped onto the same stochastic normal form.

Jaewook JooDepartment of PhysicsUniversity of [email protected]

CP31

Stochastic Asymptotic Analysis for CooperativeMultiple Motor Systems

We develop and examine a coarse-grained model for mul-tiple motors bound to a cargo, which resolves the spatialconfiguration as well as the thermal fluctuations. Throughstochastic asymptotic reductions, we derive the effectivetransport properties of the multiple-motor-cargo complex,and provide analytical explanations for why a cargo boundto two molecular motors moves more slowly at low appliedforces but more rapidly at high applied forces than when

bound to one molecular motor.

Scott McKinleyUniversity of [email protected]

Avanti AthreyaJohns Hopkins UniversityDepartment of Applied Mathematics and [email protected]

Peter R. KramerRensselaer Polytechnic InstituteDepartment of Mathematical [email protected]

John FricksDept of StatisticsPennsylvania State [email protected]

CP31

Analytical Approach to Noise-Induced Phase Syn-chronization of Chaotic Oscillators

The phase description has played a key role in analyticallyinvestigating the dynamics of limit-cycle oscillators. Here,we introduce a new type of phase description, which en-ables us to analyze various synchronization phenomena ofchaotic oscillators. Using our formulation, we study noise-induced phase synchronization of chaotic oscillators sub-jected to common random forcing. We theoretically predictprobability distributions of phase differences between twochaotic oscillators, which characterize statistical propertiesof noise-induced synchronization dynamics.

Wataru KurebayashiTokyo Institute of [email protected]

Kantaro FujiwaraSaitama [email protected]


Tohru IkeguchiSaitama [email protected]

CP31

Stochastic Resonance in a Self-Repressing Genewith Transcriptional Memory

Biochemical reaction networks are subjected to large fluc-tuations, yet underlie reliable biological functions. Theyare usually described as either deterministic or stochas-tic dynamical systems. Here, we investigate the dynamicsof a self-repressing gene using an intermediate approachbased on a moment expansion of the master equation. Wethereby obtain deterministic equations describing how non-linearity feeds back fluctuations into the mean-field equa-tions. We thus identify a region of parameter space where

124 DS13 Abstracts

fluctuations induce relatively regular oscillations.

Jingkui WangUniversite Lille [email protected]

Quentin ThommenPhLAM/Universite Lille 1, [email protected]

Marc LefrancPhLAM/Universite Lille I,[email protected]

CP31

Mathematical Analysis of Flows on Stochastic Frac-tal Networks

We present an analytical method to predict the proper-ties of the process resulting from a convolution betweena stochastic fractal network and a stochastic process. Wequantify the influence of network topology by comparinglinear (autocovariance function) and nonlinear (generalisedentropies, higher-order spectra) characteristics of the initialand resulting processes. It depends on the initial stochas-tic process and, in cases, saturates after a low number ofnetwork iterations. This has important consequences inhydrological modelling.

Christina MclemanInstitute for Complex Systems and Mathematical Biology,SUPAUniversity of Aberdeen, Scotland, [email protected]

Marco ThielUniversity of [email protected]

Doerthe TetzlaffNorthern Rivers InstituteUniversity of Aberdeen, Scotland, [email protected]

CP32

Analysis of Bifurcations and the Study of Compe-tition in Phase Oscillator Networks with Positiveand Negative Coupling

Globally coupled phase oscillators of the Kuramoto typewith positive (conformist) and negative (contrarian) cou-pling are considered in (Hong & Strogatz (HS), 2011). Wegeneralize the HS system including a phase shift in theinteraction function. The bifurcation theory and detailedstudy of the geometry of invariant manifolds is applied.The results include a rich repertoire of dynamical regimes(multistability, complex heteroclinic cycles, chaos, etc.).Some of these regimes are not possible in HS systems.

Oleksandr BurylkoInstitute of MathematicsNational Academy of Sciences, Kyiv, [email protected]

Yakov KazanovichInstitute of Mathematical Problems in Biology

Russian Academy of [email protected]

Roman M. BorisyukSchool of Computing and MathematicsUniversity of Plymouth, [email protected]

CP32

Rate-Induced Tipping Points

Open systems which are stable for any fixed external con-ditions may tip if the external conditions change too fast.Such non-autonomous instabilities are important in thenatural world, but cannot be captured by classical bifur-cations. We obtain critical rates of external forcing abovewhich the system tips. This is done numerically and ana-lytically for canonical models using an approach related tothe validity boundary of geometrical singular perturbationtheory.

Clare G. HobbsUniversity of [email protected]

Sebastian M. WieczorekUniversity of ExeterMathematics Research [email protected]

CP32

Transition Curves for the Elliptic Mathieu Equa-tion

This work investigates the equilibria and stability of a para-metrically excited pendulum when the forcing function isof an elliptic type. Stability charts are generated in theparameter plane for different values of the elliptic func-tion modulus. A method combining Floquet theory andNumerical integration is used to generate stability chartsthat are later obtained by the mean of harmonic balanceanalysis. It is shown that the size and location of the insta-bility tongues is directly dependent on the elliptic functionmodulus. Comparisons are also made between the stabil-ity charts of Mathieu equation and the elliptic Mathieuequation.

Si Mohamed Sah, Brian MannDuke [email protected], [email protected]

CP32

Periodically Forced Hopf Bifurcations

We classify the existence and stability of dynamical re-sponses to small amplitude periodic forcing of a systemnear a Hopf bifurcation point. We use forcing frequencyωf as a distinguished bifurcation parameter and vary ωf

near the Hopf frequency. This analysis uses a third orderHopf normal form truncation, though we identify regionsof parameter space where higher order terms are necessary.Time permitting, applications to physical systems will bediscussed.

Justin WiserOhio State [email protected]

DS13 Abstracts 125

Martin GolubitskyOhio State UniversityMathematical Bioscience [email protected]

CP32

On States with Two Frequencies in Ensembles ofCoupled Oscillators

I discuss a mechanism which ensures onset of oscillatorystates with two frequencies in a class of ensembles whereall elements share the intrinsic timescale and the patterncoupling is arbitrary. At the onset of oscillations, the spec-trum of the linearized flow contains not one (as usually)but two pairs of purely imaginary eigenvalues. Of the twocritical frequencies, one is typically much lower than theindividual frequency of an element, whereas the other oneis distinctly higher. Accordingly, in the nonlinear regimethe ensembles are potentially able to display both slow andfast modes of oscillations.

Michael ZaksHumboldt University, Berlin, [email protected]

CP33

A Comparison of the Local and Global Dynamicsof Monotone and Antimonotone Maps in the Plane

Monotone and antimonotone maps have widespread appli-cations in many areas of real life. For example, monotonemaps are associated to discrete competitive mathemati-cal models in Biomathematics such as the Leslie-Gowerpopulation model. Antimonotone maps are associated todiscrete mathematical models involving negative feedbackloops such as mechanical control systems and gene regula-tory networks. Although planar monotone maps are verywell-understood at this point due to the works of Hirsch,Smith, Dancer and Hess, Kulenovic and Merino etc., thesame is not necessarily true for planar antimonotone maps.In this talk, I will discuss the local and global dynamics oforbits of a class ofplanar antimonotone maps. I will alsocompare this to the local and global dynamics of orbits ofa similar class of planar monotone maps to get some veryinteresting results.

Sukanya BasuDepartment of MathematicsCentral Michigan [email protected]

CP33

Adaptation for Fast Chaos Control

In recent years, chaos control has lead to numerous applica-tions. We examine convergence speed of chaos control, anaspect which is crucial in applications such as stabilizingheart rhythms and robotics. Adaptation provides a wayto optimize convergence speed of chaos control methods[Bick, Timme, Kolodziejski. SIADS, 11(4), 1310, 2012].In particular, we focus on Predictive Feedback Control fordiscrete time dynamics and study some aspects of time-delayed feedback control of time continuous systems.

Christian BickMax Planck Institute for Dynamics and Self-Organization:[email protected]

CP33

Robustness of Periodic Windows in the Presenceof Sporadic Noise

For a dynamical system xn+1 = F (C,xn), there may beinfinitely many periodic windows, that is, intervals in C inwhich there is stable periodic behavior. However, the highperiod windows are easily destroyed with small perturba-tions. For a fixed perturbation size ε, we characterize andenumerate the ‘ε-robust windows’, that is those periodicwindows such that for some C in that window, the generalperiodic behavior persists despite noise of amplitude ≤ ε.

Madhura JoglekarUniversity of [email protected]


CP33

Trichotomy of Singularities of 2-DimensionalBounded Invertible Piecewise Rational Rotations

It is known that the singularities of 2-dimensional boundedinvertible piecewise isometric dynamical systems can beclassified as, removable, shuffling and sliding singulari-ties, based upon their geometrical traits; and that thethe removable and the shuffling singularities do not gen-erate Devaney-chaos, leaving the sliding singularity asthe only candidate for the Devaney-chaos. However, theafore-mentioned classification and the connection had beensomewhat incomplete in that the clear distinction betweenthe sliding and shuffling singularities had not been made.In this talk, the speaker will establish the complete tri-chotomy, by characterizing the self-shuffling behavior ofbounded invertible piecewise rational rotations, and leadtoward finalizing the necessary and sufficient condition ofthe Devaney-chaos.

Byungik KahngUniversity of North Texas at [email protected]

CP33

Dynamics of Certain Rational Maps of the Plane

We investigate the dynamics of rational maps of the formz �→ zn + c+ β/zd. The case when c = 0 and n = d can besolved completely because the radial dynamics decouplesfrom the angular dynamics. In the other cases, numericalinvestigation is necessary. Especially interesting are thecritical sets for n �= d and comparisons of the Julia sets forβ = 0 to the analogues for β �= 0.

Bruce B. PeckhamDept. of Mathematics and StatisticsUniversity of Minnesota [email protected]

Brett BozykUniversity of Minnesota [email protected]

CP34

Disease Persistence in Epidemiological Models:

126 DS13 Abstracts

The Interplay Between Vaccination and Migration

We consider the interplay of vaccination and migrationrates on disease persistence in epidemiological systems. Weshow that short-term and long-term migration can inhibitdisease persistence. As a result, we show how migrationchanges how vaccination rates should be chosen to main-tain herd immunity. In a system of coupled SIR models,we analyze how disease eradication depends explicitly onvaccine distribution and migration connectivity. The anal-ysis suggests potentially novel vaccination policies that un-derscore the importance of optimal placement of finite re-sources.

Jackson BurtonMontclair State [email protected]


Derek CummingsJohns Hopkins [email protected]

Ira B. SchwartzNaval Research LaboratoryNonlinear Dynamical Systems [email protected]

CP34

Epidemiological Model for X-Linked Recessive Dis-eases

We developed a discrete time, structured, mathematicalmodel describing the epidemiology of X-linked recessivediseases; the model accounts for de novo mutations anddistinct reproduction rates of procreating couples depend-ing on couples health conditions. We found the exact solu-tion to the model when de novo mutations are not relevantand negligible reproduction rates are assigned to affectedmales. Moreover, relying on Lyapunovs second method,we proved asymptotic stability properties of model equi-librium points for the case of relevant de novo mutationsand identical reproduction rates assigned to all procreatingcouples. The equilibria we obtained are a generalization ofHardy-Weinberg equilibrium.

Carmen Del VecchioUniversita Degli Studi del [email protected]

Luigi GlielmoUniversity of SannioBenevento, [email protected]

Martin CorlessSchool of Aeronautics and Astronautics, PurdueUniversityWest Lafayette, Indiana (USA)[email protected]

CP34

Modeling the Role of the Biofilm Formation in the

Development of Plant Diseases

The role of biofilms within bacterial infections has been atopic of recent interest due to the prevalence of the biofilmmode of life as well as the inability to fully eliminate thebacteria within the biofilm. Despite multiple diseases caus-ing widespread damage to the citrus, wine, and other fruitindustries, there has been little attention paid to model-ing the development and progression of these infections. Amultiphase modeling framework will be used to examinethe dynamic behavior and fluid/structure interactions ofthe biological system. Perturbation analysis will be usedto determine potential causes and tendencies of patternsdiscovered within the biofilm.

Matthew DonahueDepartment of MathematicsFlorida State [email protected]

CP34

Epidemics in Adaptive Social Networks with Tem-porary Link Deactivation

Epidemic spread depends on the topology of the networkof social contacts. Individuals may respond to the epi-demic by adapting their contacts to reduce the risk of in-fection, thus changing the network structure and affect-ing future spread. We propose an adaptation mechanismwhere healthy individuals temporarily deactivate their con-tacts with sick individuals, allowing reactivation once bothindividuals are healthy. Slow and fast network dynamicsare considered and compared to mean field analysis.

Leah ShawCollege of William and MaryDept. of Applied [email protected]

Ilker TuncThe College of William and MaryApplied Science [email protected]

Maxim S. ShkarayevCollege of William and [email protected]

CP34

A Mathematical Model Studying Mosquito-StageTransmission-Blocking Vaccines

In this talk, I will present a mathematical model of malariacontrol, particularly investigating the efficacy of imperfectvaccination. The model consists of deterministic ordinarydifferential equations. Based on our model, a backwardbifurcation very likely occurs, which suggests that using thebasic reproduction number as the threshold to eradicatethe disease is questionable. This finding might providesome valuable suggestions to health policy makers.

Ruijun ZhaoMinnesota State University, [email protected]

Jemal Mohammed-AwelValdosta State [email protected]

DS13 Abstracts 127

Nghiep HuynhMinnesota State [email protected]

CP35

Necessary Condition for Frequency Synchroniza-tion in Network Structures

We present the necessary condition that a network struc-ture should satisfy for frequency synchronization of coupledphase oscillators. A parameter called surface area describescritical network structure for synchronization. The surfacearea of a set of sites is defined as the number of links be-tween the sites within the set and those outside the set.On the basis of the condition, we can identify networks inwhich synchronization do not occur.

Fumito MoriDepartment of Information SciencesOchanomizu [email protected]

CP35

Nonuniversal Transitions to Synchrony in theSakaguchi-Kuramoto Model

TheSakaguchi-Kuramoto model is a fundamental paradigm forthe emergence of collective behavior (synchrony) in a sys-tem of non-identical oscillators that are weakly coupledby their mean field. We show that for certain unimodalfrequency distributions, this model exhibits unusual typesof synchronization transitions, where synchrony can decaywith increasing coupling, incoherence can regain stabilityfor increasing coupling, or multistability between partiallysynchronized states and/or the incoherent state can ap-pear.

Oleh Omel’chenkoWeierstrass Institute for Applied Analysis and [email protected]

Matthias WolfrumWeierstrass Institute for Applied Analysis and [email protected]

CP35

Chimera States on Periodic Spaces

Although incoherence and synchronization are the normin arrays of coupled oscillators, complex spatiotemporalpatterns such as “chimera states’—where incoherence andcoherence coexist—have been observed both computation-ally and experimentally in a wide variety of systems. I willuse an analytical approach to characterize various types ofchimera states (including stripes and spots) that appear ina two-dimensional periodic space, and discuss their chang-ing stability and bifurcations as the coupling is varied.

Mark J. PanaggioEngineering Science and Applied MathematicsNorthwestern [email protected]

Daniel AbramsNorthwestern [email protected]

CP35

The Kuramoto Model with Distributed Shear

The Kuramoto model (KM) is a paradigmatic model ofcollective synchronization, a phenomenon observed in a va-riety of natural and technological systems. An analyticalderivation of the KM is possible via phase-reduction of themean-field complex Ginzburg-Landau equation with dis-order. Nevertheless, this derivation assumes shear (non-isochronicity) is not distributed. We avoid this simplifyingassumption and obtain analytical results for the KM withdistributed shear. Remarkably we find that too much sheardiversity prevents collective synchronization.

Diego PazoInstituto de Fisica de Cantabria, [email protected]

Ernest MontbrioUniversitat Pompeu FabraBarcelona, [email protected]

CP35

Spontaneous Formation of Two-DimensionalChimera States in Oscillatory Media

Chimera states are spatiotemporal patterns in coupled os-cillatory media, where synchronized and incoherent do-mains coexist. A nonlocal coupling is believed to be in-dispensable for the formation of such states. By means ofa modified complex Ginzburg-Landau equation we demon-strate, however, that chimera states arise spontaneouslythrough a bifurcation from cluster states when just a strongglobal coupling is present. Experiments made during theelectro-oxidation of silicon confirm this theoretical predic-tion.

Lennart Schmidt, Konrad Schonleber, Katharina KrischerTechnische Universitaet Muenchen, Physik Department,Nonequilibrium Chemical [email protected],[email protected], [email protected]

Vladimir Garcia-MoralesInstitute for Advanced StudyTechnische Universitat [email protected]

CP36

Numerical Solutions of Delay Reaction-DiffusionEquations of Lotka-Volterra Type

In this paper we consider a system of delay differentialequations of Lotka-Volterra type describing the one-stagemodel of carcinogenesis mutations. A numerical schemebased on spectral postprocessing technique was employedto the simplified model from [R. Ahanger and Lin. X.B.: Multistage evolutionary model for carcinogenesis mu-tations, Electron. J. Diff. Eqns. Conf. 10 (2003), 33-53.].We check our scheme for different value of time delay andcompare the results with other available schemes.

Ishtiaq AliFaculty of Mathematics, Informatics and Mechanics,University of Warsaw, [email protected]

Xiang Xu

128 DS13 Abstracts

Department of Mathematics, Michigan State UniversityEast Lansing, MI 48824, [email protected]

CP36

Efficient Algorithms for Rigorous Integration ofDpdes

We are dealing with nonlinear partial differential equationsof dissipative type (dPDEs). Assuming that the initial con-dition is sufficiently regular the unique solution of suchsystem can be explicitly bounded using a computer algo-rithm involving the interval arithmetic. In our research wehave focused on efficient computational methods for theproblem of rigorously integrating dPDEs. We focus on acircumvention of computational difficulties by combiningthe FFT algorithm + the automatic differentiation.

Jacek CyrankaFaculty of Mathematics and Computer ScienceJagiellonian [email protected]

CP36

High Precision Periodic Orbits

Nowadays, high-precision becomes a requirement in fineanalysis of dynamical systems. We present an algorithmto locate and continue families of periodic orbits with highprecision (100-1000 digits). As example, we apply this toolto show the final spiral structure of the Copenhagen prob-lem. Finally, we combine the high-precision numerics withComputer Assisted Proof techniques in order to provide arigorous high-precision data-base of periodic orbits of theLorenz problem.

Angeles DenaUniversity of [email protected]

Alberto AbadUniversidad de [email protected]


Warwick TuckerUppsala [email protected]

CP36

Adaptive Numerical Simulation of IntracellularCalcium Dynamics Using Discontinuous GalerkinMethods

We present an adaptive in space and time simulationof intracellular calcium dynamics using discontinuousGalerkin(DG) methods. The two-dimensional parabolicsystem of partial differential equations models the diffu-sion, reaction, binding and membrane transport of calciumions within a cell. The current issues for further researchin intracellular calcium dynamics aim at moving modellingand simulation much closer to experimental data. Ourwork has addressed this challenge by implementing themodel using a highly accurate method in space and timethat goes adaptively to high order, being efficiently scal-

able. This has involved using the DG method of weightedinterior penalties and the linearly implicit Runge-Kuttamethods of Rosenbrock type. A hybrid method that cou-ples the solution of the deterministic and stochastic partof the model is adopted.

Jared O. OkiroInstitute for Analysis and Numerics, Otto-von-GuerickeUniversity, Magdeburg, [email protected]

Chamakuri NagaiahRadon Institute for Computational and AppliedMathematics,(RICAM), Linz, [email protected]

Gerald WarneckeInstitute for Analysis and Numerics,Otto-von-Guericke University, Magdeburg, [email protected]

Martin FalckeHahn Meitner [email protected]

CP36

Comparison of ODE Solvers for Parallel Uses.GPGPU and CPU

In this talk we present some results comparing RungeKutta schemes and the Taylor Series Integrator executedboth in CPU and GPGPU using different parameters: Tol-erance level, Global or Local Memory execution, and 4 and8 Bytes floating point arithmetic. We present diagrams ofCPU/GPU time vs Error in two test problems: Henon-Heiles system (dimension 4), and the same one with firstorder variational equations (dimension 16).

Marcos RodriguezCentro Universitario de la [email protected]


Fernando BlesaUniversity of [email protected]

CP37

Decomposition of Nonlinear Network Dynamics:Understanding Oscillations In Multi-Vehicle Sys-tems

Understanding the nonlinear behavior of networked sys-tems is crucial in the modern world; such systems are be-coming ubiquitous. Traditional nonlinear analysis (e.g.,center manifold reduction) becomes extremely complicatedfor systems containing large number of interacting compo-nents. In this talk we propose a novel technique wherewe decompose networked systems into nonlinear modesand carry out traditional analysis using the obtained modeequations. As a case study we analyze Hopf bifurcationsarising in vehicular traffic.

Sergei S. Avedisov

DS13 Abstracts 129

University of Michigan, Ann [email protected]

Gabor OroszUniversity of Michigan, Ann ArborDepartment of Mechanical [email protected]

CP37

Nonlinear Dynamics in the Transverse Plane ofHigh-Speed Planing Boats

When operating at high speed, planing boats are subjectto nonlinear hydrodynamic loads affecting rigid body mo-tions such as pitch, heave, and roll. Resulting instabilitiesare often a constraining factor for high-speed operations.This presentation will describe roll motion as a nonlinearsystem parametrically excited through coupling with heaveand pitch, and investigate the occurrence of nonlinear rollbehavior such as steady heel and chine walking.

John JudgeThe Catholic University of AmericaMechanical Engineering [email protected]

Carolyn JudgeUnited States Naval AcademyNaval Architecture and Ocean Engineering [email protected]

CP37

Lyapunov Stability of Rigid Bodies with FrictionalSupports

The Lyapunov stability of systems of rigid bodies interact-ing via impacts, persistent contacts and friction is poorlyunderstood. This talk addresses a model system of thistype: a single planar object with two support, for whichonly highly conservative stability conditions have beenfound earlier. By restricting my attention to ideally plasticimpacts, a nearly sharp stability condition is derived. It isalso demonstrated that intriguing phenomena of frictionalhybrid dynamics are captured by this system.

Peter L. VarkonyiBudapest University of Technology and [email protected]

CP37

An Artificial Neural Network Approach for theMass Balance of a Reactor in Steady State

The conservation of mass has been an active research areain the field of chemical engineering. In this article, a math-ematical model for mass balance of a chemical in a cylin-drical reactor is presented and the steady state case forthe mass balance of a chemical is examined by providingthe numerical solution using artificial neural network tech-nique. Numerical simulations are performed for varioushidden nodes with different number of training points andinitial weight parameters to show the dependence of resultson the number of hidden nodes, training points and initialweights. The neural network solution is also compared withthe well known finite difference method for variable stepsize and analytical solution shows the efficiency of neuralnetwork with higher accuracy. The main advantage of theproposed approach is that once the network is trained, it

allows instantaneous evaluation of solution at any desirednumber of points spending negligible computing time andmemory.

Neha YadavMotilal Nehru National Institute of Technology,[email protected]

Manoj KumarMotilal Nehru National Institute of TechnologyAllahabad, [email protected]

Kevin McfallSouthern Polytechnic State University, [email protected]

CP38

A Grand Model to Predict the Complex Combina-torial Stress Responses of Candida Albicans

Candida albicans is a major opportunistic fungal pathogen.Their ability to grow in yeast, pseudohyphal and hyphalforms help them survive, invade and kill an host organism.Their timely transition from one morphological form to an-other depends upon three major stress response pathways(SRPs): (i) oxidative, (ii) osmotic and (iii) nitrosative. Agrand mathematical model, first of its kind, encompassingthese three different SRPs is presented that can predict thesystem responses to combinatorial perturbations.

Komalapriya ChandrasekaranInstitute for Complex Systems and Mathematical BiologyInstitute of Medical Sciences, University of Aberdeen, [email protected]

Maria Carmen RomanoInstitute for Complex Systems and Mathematical BiologyInstitute of Medical Sciences, University of Aberdeen,[email protected]

Celso Grebogi, Alister J P BrownInstitute for Complex Systems and Mathematical BiologyUniversity of Aberdeen, [email protected], [email protected]

CP38

Stable Periodic Oscillations in the Biotic PyriteIron Cycle

Based on geomicrobiology literature, a model for the bioticpyrite iron cycle by Acidithiobacillus ferrooxidans bacteriais proposed. This model exhibits is some circumstances,up to two stable steady states, stable and unstable periodicorbits, Hopf, SNP and homoclinic bifurcations, as well asother dynamical structures (doubling period, chaos, etc.).It provides a possible explanation of oscillations in pH andbacteria population mentioned in the literature.

Miguel A. [email protected]

James P. KeenerUniversity of [email protected]

130 DS13 Abstracts

CP38

Nonlinearity Explains Inefficient Energy Strategyof Cancer Cells

The use of energy-inefficient metabolism is a common yetlargely unexplained property of cancer. We demonstratethat this property is in fact a consequence of a trade-offbetween the selective advantage of rapid growth and a con-current nonlinear increase in protein cost. We developed ametabolic model that incorporates protein cost and allowsus to identify candidate targets for therapeutic interven-tions. These findings provide a novel computational frame-work to analyze and potentially control cancer metabolism.

Joo Sang Lee, John Marko, Adilson E. MotterNorthwestern [email protected],[email protected], [email protected]

CP38

The Relation Between Two-Cell Model and N-CellModel on Somitogenesis of Zebrafish

Somitogenesis is the process of the development of somites.Herein, we consider two-cell and N-cell models with delaysto investigate the scenarios in zebrafish somitogenesis. Wederive the analytical theories for the oscillation-arrestedand synchronous oscillation for these two models. By theparameter regimes in our theories, we design suitable gradi-ents of degradation rates and delays in the N-cell model togenerate the chief dynamics, synchronous oscillation, trav-eling wave pattern, and oscillation-arrested, in somitogen-esis.

Kang-Ling Liao, Chih-Wen Shih, Jui-Pin TsengNational Chiao Tung [email protected], [email protected],[email protected]

CP38

Firing Threshold Manifolds: Folded Saddle Ca-nards in a Model of Propofol Anaesthesia

We investigate firing threshold manifolds in a mathemati-cal model of propofol anaesthesia, investigating the phe-nomenon of post-inhibitory rebound spiking. Propofolmodulates the decay time-scale of an inhibitory GABAasynaptic current. This system gives rise to rebound spikingwithin a specific range of propofol doses. Using techniquesfrom geometric singular perturbation theory we identify ca-nards of folded saddle-type, which form the firing thresholdmanifolds. The position and orientation of the canard sep-aratrix is propofol dependant.

John MitryUniversity of [email protected]

Michelle McCarthyDepartment of Mathematics & Center for BiodynamicsBoston [email protected]

Nancy KopellBoston UniversityDepartment of [email protected]

Martin Wechselberger

University of [email protected]

CP39

Linking Graph Motifs and Collective Spiking inNeuronal Networks

Correlations between neuron outputs (spikes) in biologicalneural networks are important characterizations of theircollective dynamics, and can determine how these dynam-ics encode input signals. We studied how spike correlationsare shaped by complex graph structures, defined via statis-tics of network motifs. We show that network-averagedspike correlations are determined by a novel set of net-work statistics – motif cumulants – which are endowedwith a combinatorial relationship similar to that betweenmoments and cumulants for random variables.

Yu HuDepartment of Applied MathematicsUniversity of [email protected]

James Trousdale, Kresimir JosicUniversity of HoustonDepartment of [email protected], [email protected]

Eric Shea-BrownDepartment of Applied MathematicsUniversity of [email protected]

CP39

Exact Collective Dynamics for a HeterogeneousNetwork of Theta Neurons

We have developed an exact model that examines the emer-gent dynamical properties of Type I neurons. Our modelconsiders individual neuronal heterogeneity with respect toexcitability and type of coupling. We employ a mean-fieldapproach and reduce the higher dimensionality of this com-plex nonlinear system to a simple exact two-dimensionaldescription. We characterize all the macroscopic states ofthe network and conduct a comprehensive bifurcation anal-ysis under which transitions in these collective states occur.

Tanushree LukeSchool of Physics, Astronomy, and ComputationalSciencesGeorge Mason [email protected]


Paul SoGeorge Mason UniversityThe Krasnow [email protected]

CP39

Core-Periphery Organization of Human Brain Dy-

DS13 Abstracts 131

namics

As a person learns a new skill, distinct synapses, brain re-gions, and networks are engaged and change over time. Tobetter understand the dynamic processes that integrate in-formation across a set of regions to enable the emergenceof novel behaviour, we measure brain activity during mo-tor sequencing and characterize network properties basedon coherent activity between brain regions. Using our re-cently developed algorithms to detect time-evolving com-munities of brain regions that control learning, we find thatthe complex reconfiguration patterns of local communitiescan be described parsimoniously by the combined presenceof a relatively stiff core of primary sensorimotor and vi-sual regions whose connectivity changes little in time and aflexible periphery of multimodal association regions whoseconnectivity changes frequently. The separation betweencore and periphery changes with the duration of task prac-tice and, importantly, is a good predictor of individual dif-ferences in learning success. This temporally defined core-periphery organization corresponds with notions of core-periphery organization established previously in social net-works: The geometric core of strongly connected regionstends to also be the temporal core of stiff regions. Wethen show using hypergraphs that the core is dominatedby the co-evolution of network edges, demonstrating thatcore regions turn on and off with the same set of partnerregions over the slow time scale of learning. Our resultsdemonstrate that core-periphery structure provides a newapproach for understanding how separable functional mod-ules are linked. This, in turn, enables the prediction of fun-damental capacities, including the production of complexgoal-directed behavior, in humans.

Mason A. PorterUniversity of OxfordOxford Centre for Industrial and Applied [email protected]

CP39

Networks of Theta Neurons with Time-Varying Ex-citability: Macroscopic Chaos, Multistability, andFinal-State Uncertainty

Using recently developed analytical techniques, we studythe macroscopic dynamics of a large heterogeneous net-work of theta neurons in which the neurons’ excitabilityparameter varies in time. We demonstrate that such pe-riodic variation can lead to the emergence of macroscopicchaos, multistability, and final-state uncertainty in the col-lective behavior of the network. Finite-size network effectsand rudimentary control via an accessible macroscopic net-work parameter is also investigated.

Paul SoGeorge Mason UniversityThe Krasnow [email protected]

Tanushree LukeGeorge Mason [email protected]


CP39

Learning Cycles in Hopfield-Type Networks withDelayed Coupling

We study the storage and retrieval of cyclic patterns inHopfield-type networks with delay using the pseudoinverselearning rule. We show that all cyclic patterns satisfyingthe transition conditions can be successfully stored and re-trieved; topology of the networks constructed from thesecyclic patterns are determined by the subspace structuresof the row spaces of the cyclic patterns; transitions fromfixed points to attracting limit cycles (cyclic patterns) aremultiple saddle-node bifurcations on limit cycles.

Chuan Zhang, Gerhard DangelmayrColorado State UniversityDepartment of [email protected], [email protected]

Iuliana OpreaDepartment of MathematicsColorado State [email protected]

MS1

Asymptotic Classification of Affine and LinearStochastic Functional Differential Equations, andApplications to Volatility Modelling

In this talk, we give a classification of the pathwise andmean-square asymptotic behaviour of affine and linearstochastic functional differential equations. In each case,stability of an underlying deterministic system plus a noiseintensity below a critical level guarantee stability, whileabove that critical level, instability ensues. The resultscan be applied to consider rates of convergence to sta-ble solutions, and to analyse when soultions of stochasticfunctional equations arising in finance have stationary so-lutions, and long–range dependence.

John ApplebySchool of Mathematical Sciences, Dublin City UniversityDublin, [email protected]

MS1

Large Deviations in Affine Stochastic FunctionalDifferential Equations

In this talk we explore the size of the running (or the run-ning maximum of the norm) of the solution of a stochasticfunctional differential equation (SFDE). In a recent paperwith Appleby and Mao, we investigated this phenomenonfor equations with a finite memory; however, the methodof proof precluded the analysis being carried through forequations with unbounded memory, or for stochastic neu-tral equations. In this work, we show that the size of thelarge deviations is the same for these classes of equationsas it is for the standard finite delay SFDE

Huizhong Appleby-WuDepartment of Mathematics, St Patrick’s College,[email protected]

MS1

Mean-square Stability of Stochastic Systems with

132 DS13 Abstracts

Memory Terms

We present a method to calculate the mean-square stabilityof dynamical systems described by Stochastic DifferentialEquations with Delay (SDDEs), which give a mathematicalformulation of problems with time-lag or memory terms, aswell as stochastic effects. We use this method to investigatethe interplay of noise and delay, including noise structure.Further, we apply our method to models arising in Neuro-science and Biology, comparing the results obtained withthe deterministic case.

Girolama NotarangeloInstitute for Stochastics, Johannes Kepler University LinzAltenberger Strasse 69, A-4040 Linz, [email protected]

MS1

Stochastic Dynamical Systems in Finance

This talk is devoted to the study of stochastic dynamicalsystems (SDS) and their applications in finance. Usually,a SDS consists of two parts: the first part is a model forthe noise path, leading to a SDS, and the second part isthe dynamics of a model. In this talk, we shall presentmany models of SDS and develop techniques in the SDSwhich can be implemented in finance. Among of thesemodels we have: stochastic Ramsay model for a capitalthat takes into account past-dependent history; geometricMarkov renewal process for a stock price with many pos-sible values; fractional Brownian motion model for a stockprice; regime-switching, delayed with Poisson jumps modelfor a stock price; delayed Heston model for a stochasticvolatility. Based on the latter model, we shall show, forexample, how to price variance and volatility swaps andhow to hedge a position with volatility swap using a port-folio of variance swaps.

Anatoliy SwishchukUniversity of [email protected]

MS2

The Role of Cardiac Tissue Anatomy duringElectric-Field Stimulation

Designing low-energy control strategies for cardiac arrhyth-mias is an area of major scientific and medical inter-est. We present experimental evidence showing that thecardiovascular tree is an anatomical substrate for field-induced wave sources observed in quiescent tissue, a mech-anism that permits Low-Energy Anti-Fibrillation Pacingto achieve considerable energy reduction compared to con-ventional defibrillation [S. Luther, F.H. Fenton et al.,Nature, 2011]. Further theoretical investigations reveala curvature-dependent sensitivity of tissue boundaries toelectric-field stimulation [PB et al., Phys. Rev. Lett.,2012], indicating the relevance of additional endocardialstructures.

Philip BittihnMax Planck Institute for Dynamics and [email protected]

MS2

Cardiac Alternans Annihilation by Model Predic-tive Control Techniques

In this research efforts, the model of alternation of action

potential dynamics is described by the small amplitudeof alternans parabolic partial differential equations (PDE)that account for electric and calcium based alternation dy-namics. We are seeking to explore model predictive controlto suppress alternans and to account for naturally presentconstraints in control of cardiac systems and to relate thisapplication to realistic physiological models.

Stevan DubljevicUniversity of [email protected]

Felicia YapariChemical and materials Engineering DepartmentUniversity of [email protected]

MS2

Continuous-time Feedback Control of Alternans inPurkinje Fibers

We use a novel model of canine Purkinje fibers whichaccurately reproduces the experimental bifurcation dia-gram of action potential duration to compare discrete-and continuous-time feedback for suppression of alternans.In the discrete-time approach, control current is appliedfor a brief time interval following each pacing stimulus.In the continuous-time approach, a piece-wise constantcontrol current is applied at all times. We show thatthe continuous-time approach suppresses alternans signifi-cantly faster compared with the discrete-time approach.

Alejandro GarzonUniversidad Sergio ArboledaBogota, [email protected]

Roman GrigorievGeorgia Institute of TechnologyCenter for Nonlinear Science & School of [email protected]

Flavio FentonGeorgia Institute of [email protected]

MS2

Coherent Structures and Nonlinear Control of 2DCardiac Tissue

Representation of cardiac tissue dynamics correspondingto spatiotemporally complex rhythms such as fibrillationas a walk through neighborhoods of a hierarchy of coherentstructures opens up unprecedented possibilities for predic-tion and control. This talk describes the computational ap-proach for identifying unstable periodic orbits representingthese coherent structures and using them and their hete-roclinic connections to guide the dynamics through phasespace, e.g., from fibrillation to normal rhythm.

Christopher MarcotteGeorgia Institute of [email protected]

Roman GrigorievGeorgia Institute of TechnologyCenter for Nonlinear Science & School of [email protected]

DS13 Abstracts 133

MS3

A Balance Model for Equatorial Long Waves

As slow dynamics often dominate in geophysical fluid mod-els, it is desirable to filter out fast motions by construct-ing simplified ‘balance’ models (e.g. the quasi-geostrophicmodel for mid-latitude dynamics). Attempts to derive itsequatorial counterpart have not been entirely successful,as Kelvin waves, which contribute significantly to tropicallow-frequency variability, are generally filtered out. I willdescribe how a balance model that captures Kelvin wavescan be constructed via asymptotic expansion.

Ian ChanUniversity of [email protected]

Theodore ShepherdUniversity of [email protected]

MS3

A Fast and Accurate Parallel-in-time Integrator forNonlinear PDEs with Scale Separation

We present a new time-stepping algorithm for nonlinearPDEs that exhibit scale separation in time. Our schemecombines asymptotic techniques (which are inexpensivebut can have insufficient accuracy) with parallel-in-timemethods (which, alone, can be inefficient for equationsthat exhibit rapid temporal oscillations). In particular, weuse an asymptotic coarse solver for computing, in serial,a solution with low accuracy, and a more expensive finesolver for iteratively refining the solutions in parallel. Wepresent examples on the rotating shallow water equationsthat demonstrate that significant parallel speedup and highaccuracy are achievable.

Terry HautUniversity of Colorado, [email protected]

Beth WingateLos Alamos National LaboratoryComputer And Computational Sciences [email protected]

MS3

Multiscale Asymptotic Approaches to RotationallyConstrained Flows

Geophysical fluid dynamical flows by their nature span alarge number of scales in both space and time. In thistalk we discuss the development of a multiscale reducedmodeling approach for rotationally constrained convectiveflows. Particularly, we present simulation results for small-scale quasigeostrophic (i) Rayleigh Benard convection and(ii) quasigeostrophic one-sided convection. The ability ofcoupling (i) and (ii) to large scale hydrostatic motions isalso discussed.

Keith JulienApplied MathematicsUniversity of Colorado, [email protected]

Antonio RubioDept. Applied MathematicsUniversity of Colorado, Boulder

rubio.colorado.edu


Geoffrey M. VasilCanadian Institute for Theoretical Astrophysics, Uni60 St. George Street, Toronto, ON, Canada M5S [email protected]

MS3

Approaching the Limit of Strong Rotation in theRotating, Stratified Boussinesq System

We investigate the dynamics of weakly stratified flow inthe presence of increasingly strong rotation rate. In realitythe limit of infinitely fast rotation (zero Rossby number)is not realized, so we consider the effect of rapid, but fi-nite rotation (Rossby number small, but finite). We usea new decomposition and direct numerical simulations toinvestigate this limiting behavior.

Jared WhiteheadUniversity of [email protected]

Beth WingateLos Alamos National LaboratoryComputer And Computational Sciences [email protected]

MS4

Experimental Observation of Chimeras in Coupled-map Lattices

While chimeras states are often found in populations ofphase oscillators, chimeras can also exist in networks ofchaotic systems with nonlocal coupling. We present theexperimental realization of these states in a feedback sys-tem which uses a liquid crystal spatial light modulator toachieve optical nonlinearity in a network of coupled chaoticmaps. We also describe scaling properties of these statesand their transition between spatial coherence and inco-herence.

Aaron M. HagerstromUniversity of [email protected]

Thomas E. MurphyUniversity of Maryland, College ParkDept. of Electrical and Computer [email protected]

Rajarshi RoyUniversity of MarylandInstitute for Research in Electronics and Applied [email protected]

Philipp HovelInstitute for Theoretical PhysicsTechnical University of [email protected]

Iryna OmelchenkoTechnische Universitat Berlin

134 DS13 Abstracts

[email protected]

Eckehard SchollTechnische Universitat BerlinInstitut fur Theoretische [email protected]

MS4

The Spectrum of Chimera States: From DiscreteMaps to Neural Systems

Chimera states exhibit surprising dynamics in compoundsystems of nonlocally coupled, identical elements that con-sist of both spatially coherent and synchronized as well asincoherent parts. Initially discovered for phase oscillators,they have been recently found in a large variety of differentmodels and have also been realized in experiments. In mypresentation, I will give an overview of the wide spectrumof possible local dynamics ranging from time-discrete mapsvia chaotic models to neural oscillators. Furthermore, I willaddress analytical results on the symmetry and stability ofthese hybrid states.

Philipp HovelInstitute for Theoretical PhysicsTechnical University of [email protected]

MS4

Chimera in Space-time Representation of Opto-electronic Nonlinear Delay Dynamics

Delay dynamical systems are known to have a space-timeinterpretation. We propose to use this feature for the questof experimental Chimera. A benchmark optoelectronic de-lay oscillator is considered as the physical setup intendedto emulate a high dimensional spatio-temporal dynamics ofcoupled virtual nodes. Theoretical analysis, as well as nu-merical simulations, are proposed to identify the temporaland amplitude parameter conditions under which Chimeracould be obtained in an experimental delay dynamics.

Laurent LargerUniversite de Franche-ComteFEMTO-ST institute / Optics [email protected]

Bogdan PenkovskyiNational University [email protected]

Yuri MaistrenkoInstitute of Mathematics, NAS of UkraineTereschenkivska Str. 3, 01601 Kiev, [email protected]

MS4

Chimera States for Repulsively Coupled Phase Os-cillators

We discuss the appearance of chimera states for repulsivelycoupled phase oscillators of the Kuramoto-Sakaguchi type,i.e., when the parameter α > π/2 and hence, the net-work coupling works against synchronization. We find thatchimeras exist in a wide region of the parameter space as acascade of the states with increasing number of the regionsof irregularity - chimeras heads. They grow from the so-called multi-twisted states in three different scenarios: via

snic, blue-sky catastrophe, and homoclinic transition.

Yuri MaistrenkoInstitute of Mathematics, NAS of UkraineTereschenkivska Str. 3, 01601 Kiev, [email protected]

MS5

May We Interpret Swimming as a Limit Cycle?

There is something periodic and stable about the motion ofa fish swimming. Specifically, it seems natural to surmisethat swimming is a limit cycle. In this talk I will lever-age various Lie group symmetries to find a space on whichthis interpretation makes sense. The resulting observationscan be abstracted, and then specialized to a number of dis-sipative Lagrangian systems and perhaps used to analyzeother types of locomotion including terrestrial locomotionand pumping of fluids.

Henry O. JacobsImperial College [email protected]

MS5

Pinch-off and Optimal Vortex Formation in Biolog-ical Propulsion

A wide class of swimming animals propel themselves byforming vortex rings and loops. It is known that vor-tex rings cannot grow indefinitely, but rather ‘pinch-off’once they reach their physical limit, and that a decreasein efficiency of fluid transport is associated with pinch-off.Therefore, in this study, we consider models for the vortexrings in the wakes of swimming animals, and characterizetheir perturbation response in order to assess their opti-mality.

Clara O’Farrell, John O. [email protected], [email protected]

MS5

A Variational, Second-order Integrator for PointVortices on the Sphere

I will introduce a novel formulation of point vortex dynam-ics on the sphere using unit quaternions. In this way, pointvortex dynamics on the sphere is recast a Schrodinger-likeequation, which facilitates the construction of geometricalnumerical integrators. I will derive this formulation usingthe Hopf fibration, and I will derive a numerical integra-tor with good long-term qualitative behavior, which willbe illustrated on the spherical von Karman vortex street.

Joris Vankerschaver, Melvin LeokUniversity of California, San DiegoDepartment of [email protected], [email protected]

MS5

Computationally Tractable Tools for the Identifica-tion of Hybrid Dynamical Models of Human Move-ment

Given the loss of freedom common to injuries arising dueto falls, the development of techniques capable of pinpoint-

DS13 Abstracts 135

ing instabilities in gait is critical. Devising an algorithmcapable of detecting such deficiencies requires employingmodels rich enough to encapsulate the discontinuities inhuman motion. Hybrid systems, which describe the evo-lution of their state both continuously via a differentialequation and discretely according to a discrete input, arecapable of representing such motion. This talk begins byillustrating how a sequence of contact point enforcementsalong with a Lagrangian intrinsic to the human completelydetermines a hybrid system model. The detection of con-tact point enforcement is then transformed into an optimalcontrol problem for switched systems which is solved by re-laxing the discrete input and performing optimization overa relaxed discrete input space. The utility of this approachis illustrated by considering several examples.

Ram VasudevanUniversity California [email protected]

MS6

Spectral Variational Integrators

Using techniques from Galerkin variational integrators, weconstruct a scheme for numerical integration that con-verges geometrically, and is symplectic and momentumpreserving. Furthermore, we prove that under appropri-ate assumptions, variational integrators constructed usingGalerkin techniques will yield numerical methods that arein a certain sense optimal, converging at the same rateas the best possible approximation in a certain functionspace. We further prove that certain geometric invariantsalso converge at an optimal rate.

Melvin Leok, James HallUniversity of California, San DiegoDepartment of [email protected], [email protected]

MS6

Controlled Lagrangians and Stabilization of Dis-crete Spacecraft with Rotor

This talk discusses the method of controlled Lagrangiansfor discrete mechanical systems and its application to theproblem of stabilization of rotations of a spacecraft aboutits intermediate inertia axis. The distinction between thestability conditions for a continuous-time system and itsdiscretization will be discussed. It will be shown that sta-bility of the discrete system is sufficient for stability of itscontinuous counterpart but not vice versa.

Yuanyuan PengDepartment of MathematicsClaflin [email protected]

Syrena HuynhNorth Carolina State UniversityDepartment of Mechanical [email protected]

Dmitry ZenkovNorth Carolina State UniversityDepartment of [email protected]

Anthony M. BlochUniversity of Michigan

Department of [email protected]

MS6

The Hamilton-Pontryagin Principle and Lie-DiracReduction on Semidirect Product

We consider the Hamilton-Pontryagin variational principleon Lie groups and its associated Lie-Dirac reduction, whichmay yield the reduced implicit Euler-Poincare equations.Especially, we focus on the case of the variational principlewith advective parameters as well as reduction of Diracstructures on semidirect product. Finally, we show someillustrative examples of rigid body and fluids.

Hiroaki YoshimuraWaseday [email protected]

Francois Gay-BalmazEcole Normale [email protected]

MS6

Variational Structures for Hamel’s Equations

Hamel’s equations are an analogue of the Euler-Lagrangeequations of Lagrangian mechanics when the velocity ismeasured relative to a frame unrelated to the system’s localconfiguration coordinates. This formalism is particularlyuseful in nonholonomic mechanics. We will discuss thevariational structures associated with Hamel’s equations,along with applications to nonholonomic integrators.

Dmitry ZenkovNorth Carolina State UniversityDepartment of [email protected]

Kenneth BallNorth Carolina State UniversityDeppartment of [email protected]

Anthony M. BlochUniversity of MichiganDepartment of [email protected]

MS7

Homoclinic Bifurcations Leading to Merging andExpansion of Chaotic Attractors

Chaotic dynamics in piecewise smooth maps may persistunder parameter variations. Still, the chaotic domain insuch maps may be well-structured by crisis bifurcations,caused by homoclinic bifurcations of unstable cycles. Wediscuss how the effect of these bifurcations depends on theproperties of the cycles and how the resulting generic bi-furcation scenarios depend on the properties of the map(which may be continuous or discontinuous, may possessone or several border points).

Viktor AvrutinIPVSUniversity of [email protected]

136 DS13 Abstracts

MS7

Global Attractors for Slowly Non-DissipativeEquations with Jumping Nonlinearities

This talk presents new results in the study of non-compactglobal attractors for slowly non-dissipative reaction-diffusion equations. We analyze grow-up equations withasymptotically asymmetric growth rates, where the opera-tor controlling the behavior at infinity contains a jump-ing nonlinearity. We present bifurcation, stability, andnodal property results which determine the connecting or-bit structure as well as how the jumping nonlinearity atinfinity introduces Fucik spectrum theory to the analysisin the sphere at infinity.

Nitsan Ben-GalInstitute for Mathematics and its ApplicationsUniversity of [email protected]

Kristen MooreUniversity of [email protected]

Juliette HellInstitut fuer MathematikFreie Universitaet [email protected]

MS7

Dynamics at Infinity for a PDE with Jumping Non-linearity

A jumping nonlinearity naturally arises in the study ofthe dynamics at infinity for slowly nondissipative reaction-diffusion equations ut = Δu+f(u) where f goes to infinityalong different slopes b+ and b− at positive and negativeinfinity. Although the behavior at infinity is well under-stood in the symmetric case b+ = b−, lack of smoothnessin the nonsymmetric case jumbles the classical picture ofheteroclinic connections. The behavior near the sphere atinfinity is described via Poincare ”compactification” .

Juliette HellFreie Universitat BerlinInstitut fur [email protected]

Nitsan Ben-GalInstitute for Mathematics and its ApplicationsUniversity of [email protected]

MS7

Grazing Induced Bifurcations in Impact Oscilla-tors: Theory and Experiments

Abstract not available at time of publication.

Marian WiercigrochUniversity of AberdeenKing’s [email protected]

MS8

Random Dynamical Systems Approach to the

Problem of Gene Expression

A genetic regulatory network (GRN) is a collection of DNAsegments in a cell which interact with each other throughtheir RNA and protein expression products, thereby gov-erning the rates at which genes in the network are tran-scribed into mRNA. These interactions are made by specialproteins called transcription factors which bind the DNA atthe promoter site to regulate the rate that specific gene tar-gets are expressed. Much theoretical work on the structureof GRN focused on the static aspects of networks (topolog-ical or statistical properties). However, general studies ofthe dynamics (the processes that take place on a network)are fairly rare. In this work we propose an approach to thedynamics of genetic regulatory networks, whcih moreoveraccounts for the noise observed in the transcription pro-cess, by modelling the interaction of a transcription factorwith the promoter region of a gene through suitable ran-dom dynamical systems resembling the Michaelis-Mentenenzymatic kinetics.

Fernando AntoneliSao [email protected]

Renata Carmona, Francisco [email protected], [email protected]

MS8

Wilson Networks for Binocular Rivalry

In rivalry the two eyes of a subject are presented withtwo images. Usually, the subject reports seeing the twoimages alternating. Wilson proposed a class of neuronalnetworks for multiple competing patterns. The neuronalnetwork has learned patterns that help define the networkstructure. These networks also support patterns that werenot learned, which we call derived. There is evidence forperception of derived patterns in binocular rivalry experi-ments. We consider Wilson networks corresponding to ex-periments of Kovacs, Papathomas, Yang, and Feher. Thefirst experiment is the noted monkey-text rivalry experi-ment. We show that a simple Wilson model makes ex-pected the surprising outcome. The second experimentconcerns rivalry between dots of different colors. We con-struct a Wilson network for the dots experiment and usesymmetry to make predictions regarding states that a sub-ject might perceive. This is joint work with C. Diekmanand Y. Wang.

Martin GolubitskyOhio State UniversityMathematical Biosciences [email protected]

MS8

Normal Forms and Bifurcations of Semigroup Net-works

The local bifurcation analysis of network dynamical sys-tems is complicated by the fact that the normal form ofa network near a local equilibrium may not have a nicenetwork structure. We resolve this issue here by introduc-ing so-called semigroup networks. It turns out that suchnetworks are determined by a semigroup of symmetries.In particular, the synchronous solutions and the spectraldegeneracies of any network are determined by hidden sym-

DS13 Abstracts 137

metries in an appropriate semigroup network.

Bob Rink, Jan SandersVU University [email protected], [email protected]

MS8

Rigid Phase-shifts in Periodic Solutions of NetworkSystems

Networks of differential equations can be described ab-stractly by a directed graph whose nodes correspond tosystems of differential equations and arrows correspondto coupling between the systems. Suppose that x(t) isa T -periodic solution and xi(t) and xj(t) are the coordi-nates of x(t) corresponding to nodes i and j. The twonodes are phase-related if there exists 0 ≤ θ < 1 such thatxj(t) = xi(t + θT ). The phase relation θ is rigid if it re-mains unchanged on perturbation of the coupled system.In this talk we discuss joint work with M. Golubitsky andD. Romano that shows how rigid phase-shifts are related tonetwork architecture (the graph) and network symmetries.

Yunjiao WangRice Univ. [email protected]

MS9

Stochastic Prediction and Control in Time-dependent Dynamical Systems

We consider the problem of stochastic prediction and con-trol in a time-dependent stochastic environment, such asthe ocean, where escape from an almost invariant regionoccurs due to random fluctuations. In particular, a con-trol strategy is formulated that utilizes knowledge of theunderlying flow and environmental noise. The control pol-icy enables mobile sensors to autonomously and efficientlypursue a variety of tasks by maintaining a desired distribu-tion in the environment. The control strategy is evaluatedwith experimental data.

Eric ForgostonMontclair State UniversityDepartment of Mathematical [email protected]


Ani HsiehDrexel [email protected]


Philip YeckoMontclair State [email protected]

MS9

Relatively Coherent Sets as a Hierarchical Parti-tion Method in Time-dependent Chaotic Dynami-

cal Systems

We present an extension of finite-time coherent pairs intime-dependent dynamical systems to generalize the con-cept to hierarchically defined relatively coherent sets. Theidea is based on specializing the finite-time coherent sets touse relative measures restricted to sets that are developediteratively and hierarchically in a tree structure of parti-tions and the resulting restricted Frobenius-Perron opera-tors. Several examples are used to illustrate our method.

Tian MaDepartment of Mathematics and Computer ScienceClarkson [email protected]

Erik BolltClarkson [email protected]

MS9

Revealing the Phase Portrait of Aperiodic TimeDependent Dynamical Systems: New Tools andApplications

A very useful approach for studying dynamical systems isbased on Poincar ideas of seeking geometrical structures onthe phase space that divide it into regions correspondingto trajectories with different dynamical fates. These ideashave demonstrated to be very powerful for the descriptionof transport in purely advective flows. We study the perfor-mance of recently proposed tools, the so called Lagrangiandescriptors, for achieving phase portrait representations ingeophysical flows. We analyze the convenience of differentdescriptors from several points of view and compare out-puts with other methods proposed in the literature. Wediscuss applications of these tools on oceanic and atmo-spheric realistic datasets.

Ana M. ManchoInstituto de Ciencias MatematicasConsejo Superior Investigaciones [email protected]

Stephen WigginsUniversity of [email protected]

Jezabel CurbeloIntituto de Ciencias Matematicas (ICMAT), [email protected]

Carolina MendozaUniversidad Politecnica de [email protected]

MS9

Chaotic Advection in a Steady, Three-dimensional,Ekman-driven Eddy

We investigate chaotic advection within a three-dimensional, steady or steady, rotating-cylinder flow,driven by a surface stress. A high-resolution spectral el-ement model is used to map out the barriers, manifolds,and resonances. Invariant tori for cases with O(1) Ekmannumber are found to be remarkably stable to the perturba-tion. A formula for the resonance width is derived, and thisand a version of the KAM theorem are used to interpret

138 DS13 Abstracts

our findings.

Lawrence Pratt, Irina RypinaWoods Hole Oceanographic [email protected], [email protected]

Tamay OzgokmenUniversity of Miami/[email protected]

MS10

Truth-model Synchronization and Model-modelSynchronization: A Path to Intelligent CompactRepresentation of a High-dimensional Reality

Predictive computational models that assimilate new ob-servations of a real system as they run are intended tosynchronize with that system, defining a new applicationof chaos synchronization to the problem of machine percep-tion. A recent extension is to arrange for several alternativemodels of the same reality to synchronize with one another,a strategy suggestive of conscious mental processing, thatgives improved modeling with ODE systems and a PDErepresenting the large-scale atmospheric circulation.

Gregory S. DuaneNational Center for Atmospheric [email protected]

MS10

Improvement in Predictive Modeling by CouplingImperfect Models

A supermodel is an interconnected ensemble of existingimperfect models of a real, observable system, intended tocombine the best features of the individual models. Theconnections between the models can be learned from ob-servational data using methods from machine learning. Wepresent new efficient, robust and scalable learning strate-gies to optimize supermodels for dynamical systems of lowcomplexity, in particular for the case where connection co-efficients appear only in equations for unobserved variables.

Carsten GrabowPotsdam Institute for Climate Impact [email protected]


MS10

Synchronous Coupling of Large Climate Models forImproved Climate Change Projection

Models used internationally to project climate change givedivergent predictions in regard to the magnitude of glob-ally averaged warming and in regard to specific regionalchanges. An “interactive ensemble of three different globalclimate models (GCMs) has been formed using inter-modeldata assimilation. Even with crude assignment of assim-ilation weights based on historical data, the resulting su-permodel promises improved performance as compared to

any single model or weighted average of model outputs.

Joseph J. TribbiaNat’l Center for [email protected]

Alicia KarspeckNational Center for Atmospheric [email protected]

MS10

Climate Model Intercomparison at the DynamicsLevel

We address how well models agree when it comes to dy-namics they generate, by adopting an approach based onclimate networks. We considered 98 runs from 23 modelsand constructed networks for the 500 hPa, surface air tem-perature (SAT), sea level pressure (SLP), and precipitationfields for each run. We find that with possibly the excep-tion of the 500 hPa filed, the consistency for the SLP andespecially SAT and precipitation fields is questionable.

Karsten SteinhaeuserDepartment of Computer Science and EngineeringUniversity of Minnesota, Twin [email protected]

Anastasios TsonisUniversity of Wisconsin, [email protected]

MS11

On the Generation of Beta Oscillations in the Sub-thalamic Nucleus-globus Pallidus Network

A key pathology of Parkinsons disease is the occurrenceof persistent beta oscillations. We investigate an earliermodel of the network composed of subthalamic nucleus(STN) and globus pallidus (GP) that identified the con-ditions under which this circuit could generate beta oscil-lations. We derive stability conditions that are valid forarbitrary synaptic transmission delays. Our analysis ex-plains how and why changes in inputs to the STN-GP net-work influence circuit oscillations.


MS11

Striatum as a Potential Generator of Beta Oscilla-tions in Parkinson’s Disease

Prominent beta frequency oscillations arise in the basalganglia in Parkinsons disease. The dynamical mechanismsgenerating these oscillations are unknown. Using math-ematical models, we show that robust beta oscillationscan emerge from interactions between striatal mediumspiny neurons. The interaction between the membraneM-current and the synaptic GABAa current provides acellular-level interaction promoting the formation of thebeta oscillation. Experimental testing of our model innormal, mouse striatum resulted in pronounced, reversible

DS13 Abstracts 139

beta oscillations

Michelle McCarthyDepartment of Mathematics & Center for BiodynamicsBoston [email protected]

Xue HanBoston UniversityDepartment of Biomedical [email protected]

Ed BoydenMIT Media [email protected]

Nancy J. KopellBoston UniversityDepartment of [email protected]

MS11

Dynamical Circuits Coupling Between Basal Gan-glia and Cerebral Cortex

Elevated level of synchrony in the beta band across cortico-basal ganglia-thalamo-cortical circuitry is related to themotor symptoms of Parkinsons disease. We will discuss ourstudies of phase synchronization between cortical and basalganglia oscillatory neural activity, in particular we considerthe temporal patterns of this synchronization and the useof the mathematical models to investigate the mechanismsunderlying observed synchronous dynamics.

Leonid RubchinskyDepartment of Mathematical SciencesIndiana University Purdue University [email protected]

Sungwoo AhnIndiana University Purdue University [email protected]

Elizabeth ZauberIndiana University School of [email protected]

Robert WorthDepartment of NeurosurgeryIndiana University School of [email protected]

MS11

Intrinsic Dynamics of Dopamine Neurons: Model-ing and Experiments

Dopaminergic (DA) neurons are slow intrinsic pacemakersthat undergo depolarization block upon stimulation. In re-sponse to several pharmacological manipulations, they alsoexhibit bursting and tonic firing. These activities are rele-vant to the dysfunctional dopaminergic signaling observedin Parkinson’s disease and schizophrenia. We present acomprehensive multicompartment model of DA neurons touncover the ionic basis of the signaling described above.Furthermore, we use a reduced three-compartment modelto study its underlying dynamics using bifurcation analy-

sis.

Na YuLouisana State University - Health Science CenterDepartment of Cell Biology and [email protected]

MS12

Instability in Nearly Integrable Hamiltonian Sys-tems with Three Degrees of Freedom

This talk is to sketch the proof of Arnold diffusion in nearlyintegrable Hamiltonian systems with three degrees of free-dom and related problems.

Chong-Qing ChengNanjing [email protected]

MS12

Geometric and Topological Structures in Hamilto-nian Dynamics

An important problem in the study of Hamiltonian systemsis to identify geometric/topological templates that orga-nize the dynamics, and to develop constructive methodsthat can applied to concrete examples and implemented inrigorous numerical experiments. We will present severalmodels of unstable Hamiltonian systems, and will surveysome geometric, topological, and variational methods thatcan be used to describe the dynamics. We will discuss someapplications to celestial mechanics, engineering, populationdynamics, and medicine.

Marian GideaNortheastern Illinois [email protected]

MS12

Low-dimensional Dynamics in Nnonlinear WaveSystems

The nonlinear Schrdinger equation (NLS) is a ubiquitousmodel in mathematical physics. In diverse settings–lightpropagation in coupled nonlinear waveguides and inducedvortex motion in Bose Einstein condensate, the dynamicsare well-described by small systems of Hamiltonian ODE.Using Hamiltonian reductions and normal form analysis,we investigate bifurcations discover hidden and surprisingstructures in the dynamics of these ODE models and relatethem to direct numerical simulation of NLS.

Roy GoodmanNew Jersey Institute of [email protected]

MS12

Regularizing Transformations in the Planar Three-body Problem

I will describe an interesting way to regularize all three bi-nary collisions and blow-up the triple collision in the planarthree-body problem and discuss progress on extensions tothe planar four-body problem.

Richard MoeckelUniversity of [email protected]

140 DS13 Abstracts

Richard MontgomeryUniversity of California at Santa [email protected]

MS12

Small Generalized Breathers with ExponentiallySmall Tails for Klein-Gordon Equations

Breathers are solutions to PDEs which are periodic in timeand localized in space. One famous example is the familyof the breathers of the sine-Gordon equation. On the onehand, as shown by Birnir-McKean-Weinstein and Denzler,these breathers are rigid in the sense that they do not per-sist under small perturbations to the sine-Gordon equation.On the other hand, the formal analysis by Segur-Kruskal,for the φ-4 model, which can be viewed as a perturbationto the sine-Gordon equation for small amplitude waves, theobstacle to solving the equation for breathers is exponen-tially small with respect to the amplitude of the breathers.In the talk, we consider a class of Klein-Gordon equationand show that generically there exist small breathers withexponentially small tails.

Chongchun ZengGeorgia [email protected]

Nan LuUniversity of Massachusetts at [email protected]

MS13

Data-driven Mesoscopic Neural Modelling

This presentation will discuss methods for developingsubject-specific mesoscopic neural models. The ability tocreate subject-specific models will enable estimation of nor-mally hidden aspects of physiology. Imaging physiologicalparameters will lead to a greater understanding of diseasesand provide new targets for novel therapies. The model-data fusion framework in this presentation is based on non-linear Kalman filtering. In particular, we will demonstrateestimation accuracy using synthetic data before showingresults from real intracranial EEG data.

Dean R. Freestone, David GraydenUniversity of Melbourne, Australia& The Bionics Institute, Melbourne, [email protected], [email protected]

Mark CookSt. Vincent’s Hospital, Melbourne, Australia& The Bionics Institute, Melbourne, [email protected]

Dragan NeicUniversity of Melbourne, [email protected]

MS13

Optimal Control of Spiking Neuron Ensembles

Altering neuronal spiking activity using external stimuliis a subject of active research and is imperative for wide-ranging applications from the design of neurocomputers toneurological treatment of Parkinson’s disease. We studythe control of an ensemble of neuron oscillators describedby phase models. We examine controllability of a neuron

ensemble and derive time-optimal and minimum-energycontrols for spiking a neuron ensemble by using a robustcomputational method based on pseudospectral approxi-mations.

Jr-Shin Li, Isuru DasanayakeWashington University in St. [email protected], [email protected]

Justin RuthsSingapore University of Technology & [email protected]

MS13

Transient Neurodynamics and the Role of SensoryDead Zones

Sensory thresholds can produce complex transient neuro-dynamics. We illustrate this phenomenon through a studyof stick balancing at the fingertip. Although stick bal-ancing stability is well accounted for by the presence oftime-delayed feedback, the experimentally-observed tran-sient dynamics (Weibull-type survival functions, intermit-tency, Lvy-distributed variables) are most easily explainedby incorporating a sensory threshold into the control mech-anism. Sensory thresholds and transient dynamical phe-nomena necessitate a reconsideration of current models forneural computation and control.

John MiltonClaremont [email protected]

Gabor StepanDepartment of Applied MechanicsBudapest University of Technology and [email protected]

Tamas InspergerBudapest University of Technology and EconomicsDepartment of Applied [email protected]

MS13

Controlling Populations of Neurons

There is evidence that an effective treatment for neurologi-cal diseases such as Parkinson’s disease and epilepsy wouldbe to desynchronize appropriate populations of neurons, forexample through the use of deep brain stimulation. Thistalk will serve as an overview of different methods whichhave been proposed to accomplish this goal, with an em-phasis on methods which exploit ideas from the theory ofdynamical systems.


MS13

Symmetry in the Observability and Controllabilityof Neuronal Networks

The theory of observers is a mature one for linear systems.But it is far less developed for nonlinear systems, and veryincomplete for nonlinear networks. Nevertheless, there isgrowing interest in model-based control of neural systems,

DS13 Abstracts 141

and accordingly, we have begun to investigate the effect ofnetwork symmetries on the observability and controllabil-ity of neuronal networks.

Steven J. SchiffPenn State UniversityCenter for Neural [email protected]

Andrew Whalen, Sean BrennanPenn State [email protected], [email protected]


MS14

An Overview of Localized Pattern Formation, withComments on Non-variational and Non-local Prob-lems

I will introduce the minisymposium by reviewing the un-derlying structure that supports the existence of localizedstates near subcritical pattern-forming instabilities. Com-ments on recent work concerning non-variational or non-local terms in model equations will follow; some of this isjoint work with John Burke (Boston).

Jonathan DawesUniversity of [email protected]

John BurkeBoston [email protected]

MS14

Exponential Asymptotics and Homoclinic Snaking

Homoclinic snaking of localized patterns has been observedin a variety of experimental and theoretical contexts. Thephenomenon, in which a multiplicity of localized states ex-ists within an exponentially small parameter range, is dueto the slowly varying amplitude ’locking’ to the underly-ing pattern. We show how conventional methods, such asmultiple scales near bifurcation, must be extended to incor-porate exponentially small effects if a complete asymptoticdescription of snaking behaviour is to be achieved.

Andrew DeanUniversity of Leedsn/a

Paul C. MatthewsUniversity of [email protected]

Stephen M. CoxUniversity of NottinghamSchool of Mathematical [email protected]

John KingUniversity of [email protected]

MS14

Radially Symmetric Spot Solutions for the Swift–Hohenberg Equation

The existence of stationary localized spots for the pla-nar and the three-dimensional Swift–Hohenberg equationis proved using geometric blow-up techniques. The spotshave a much larger amplitude than that expected from aformal scaling in the far field. One advantage of the geo-metric blow-up methods is that the anticipated amplitudescaling does not enter as an assumption into the analysisbut emerges during the construction. The stability of thesesolutions will also be addressed.

Scott McCallaUniversity of California Los [email protected]

Bjorn SandstedeBrown Universitybjorn [email protected]

MS14

Localized Patterns in Systems with Two LengthScales, and Oscillons in Parametrically Forced Sys-tems

We present two examples of one-dimensional localized pat-terns. In the first, the model system is unstable to twowavelengths and we find patterns with one wavelength em-bedded in a background of patterns with the other wave-length. In the second example, the model system is para-metrically forced and the patterns are analogues of the os-cillons found in Faraday wave experiments. In both cases,we analyse the system by carrying out long-wavelength ex-pansions.

Abeer Al-Nahdi, David Bentley, Jitse NiesenUniversity of [email protected], [email protected],[email protected]

Alastair M. RucklidgeDepartment of Applied MathematicsUniversity of [email protected]

Thomas WagenknechtUniversity of Leedsn/a

MS14

Spatial Patterns in Shear Flows

When shear flows become turbulent spatio-temporal pat-terns emerge in the chaotically fluctuating flow. Those pat-terns such as localized turbulent spots or laminar-turbulentstripes appear to be captured by spatially localized exactinvariant solutions of the 3D Navier-Stokes equations. Spe-cific equilibrium and traveling wave solutions are organizedin a snakes-and-ladders structure strikingly similar to thatobserved in simpler pattern-forming PDE systems, suggest-ing that well-developed theories of patterns in simpler PDEmodels carry over to transitional turbulent flows.

Tobias SchneiderMax Planck Institute for Dynamics and Self-Organization,[email protected]

142 DS13 Abstracts

John GibsonUniversity of New [email protected]

MS15

Identification and Tracking of Optimally CoherentSets in the Ocean and Atmosphere via Transfer Op-erators

Optimally coherent sets are those sets that are the most ef-ficient transporters of geophysical flow mass. We describea recent numerical method that uses Lagrangian informa-tion to detect and track optimally coherent sets in time-dependent geophysical flows. We illustrate the new ap-proach by tracking Agulhas rings, and accurately deter-mining the locations of the Antarctic polar vortex. Themethod works naturally in two- and three- dimensions, andcan handle both advective and advective/diffusive dynam-ics.

Gary FroylandUniversity of New South [email protected]

Christian HorenkampChair of Applied MathematicsUniversity of [email protected]

Adam MonahanSchool of Earth and Ocean SciencesUniversity of [email protected]

Vincent RossiUNSW, Australia,[email protected]

Naratip SantitissadeekornNorth Carolina Chapel [email protected]

Alex Sen GuptaUNSW, [email protected]

Erik van SebilleUniversity of New South [email protected]

MS15

Scale-dependent Relative Dispersion and Applica-tion to Submesoscale Lagrangian Parametrization

The scale-dependent Finite Scale Lyapunov Expo-nent(FSLE(delta)) is a metric closely related to tracer dis-persion problems as it differentiates the scales of disper-sion. It is also particularly suited to investigate the dis-persive regimes at the submesoscales, which tends to beunderestimated in numerical models and can help in thedevelopment of Lagrangian parametrization. Results willbe presented on existing Lagrangian subgridscale modelsadapted to tackle the muti-scale ocean transport problem.

Angelique C. HazaMPO, RSMAS, University of [email protected]


Annalisa GriffaCNR, Lerici, [email protected]

Zulema [email protected]

Leonid Piterba PiterbargU of Southern [email protected]

MS15

Space-Filling Lattices of 3D Vortices Created bythe Self-Replication of Critical Layers in LinearlyStable, Shearing, Stratified, Rotating Flows

A space-filling lattice of 3D vortices spontaneously formsin linearlystable, rotating, stratified shear flows. The lat-tice is due to a new family of easily-excited critical layerswith singular vertical velocities. The layers draw energyfrom the background shear and roll-up into vortices thatgenerate waves. The waves excite new critical layers andvortices. The vortices nonlinearly and self-similarly repli-cate to create a vortex lattice. This self- replication occursin stratified Couette flows and in protoplanetary disks.

Philip S. MarcusUniv. of California at BerkeleyDept. of Mech. [email protected]

Chung-Hsiang Jiang, Suyang Pei, Pedram HassandadehUniversity of California at [email protected], [email protected],[email protected]

MS15

Hyperbolic Lagrangian Coherent structures(LCSs) and LCS-cores

Underlying the flow are structures, broadly known as La-grangian Coher- ent structures (LCSs), which form theskeletons of passive tracer patterns. Some LCS can sus-tain highly attracting cores whose identification can helppredicting the development of an instability in a tracer dis-tribution. Here I exemplify this using data collected dur-ing the Deepwater Horizon oil spill and the eruption of theEyjafjallajokull volcano in 2010, and a Lagrangian drifterexperiment in Gulf of Mexico recently carried out.

M. Josefina OlascoagaUniversity of [email protected]


Laura FiorentinoUniversity of Miami, [email protected]

Francisco J. Beron-Vera

DS13 Abstracts 143


MS15

Lagrangian Fronts and Potential Fishing Grounds

Lagrangian fronts in the ocean delineate boundaries be-tween waters with different Lagrangian properties. We pro-pose a general method to identify them in any velocity fieldbased on computing synoptic maps of the drift of synthetictracers and other indicators. It is shown with the altimetricgeostrophic velocity fields that fishing grounds with max-imal catches are located mainly along those Lagrangianfronts where converge dissimilar waters of different originand history. The proposed method may be applied to fore-cast potential fishing grounds for pelagic fishes in differentregions.

S.V. PrantsPacific Oceanological Institute of the Russian Academy [email protected]

M.V. BudyanskyPacific Oceanological Institute of the Russian Academyof [email protected]

M.Yu. UleyskyPacific Oceanological Institute of the Russian Academy [email protected]

MS16

Stabilization of Difference Equations with Stochas-tic Perturbations

A map which experiences a period doubling route to chaos,under a stochastic perturbation with a positive mean, canhave a stable blurred 2-cycle for large enough values of theparameter. The limit dynamics of this cycle is described,and it is demonstrated that most well-known populationdynamics models (for example, Ricker, truncated logistic,Hassel and May, Bellows maps) have this stable blurred2-cycle. For a general type of maps, in addition, there maybe a blurred stable area near the equilibrium.

Elena BravermanDepartment of Mathematics & StatisticsUniversity of [email protected]

Alexandra RodkinaThe University of the West IndiesMona, Kingston, [email protected]

Leonid BravermanAthabasca University andSt. Mary’s University College, AB, [email protected]

MS16

Stochastic Effects in Non-normal Systems: An Ex-ample from Ecology

Consider the linearisation of a predator-prey model aroundan equilibrium representing species coexistence. The dy-

namics are governed by a non-normal coefficient matrix,which may display a large transient response to initial-value perturbation even when the equilibrium is asymptot-ically stable. We examine the effect of persistent stochasticperturbation of each species on mean-square dynamics, ex-tending to the stochastic case measures of asymptotic andtransient response to initial value perturbations proposedby Neubert & Caswell (1997).

Conall KellyDepartment of Mathematics and Computer ScienceThe University of the West Indies, Mona, Kingston,[email protected]

MS16

The Poincare Map of Randomly Perturbed Peri-odic Motion

For a system of differential equations in Rn perturbed bysmall white noise, we construct the Poincare map in thevicinity of a stable limit cycle. We show that the timeof the first exit from a small neighborhood of the fixedpoint of the map is approximatelly geometric and provideapplications of this result to the analysis of bursting andmixed-mode oscillations in neuronal models. This is jointwork with Pawel Hitczenko.

Georgi S. MedvedevDrexel [email protected]

MS16

On Discrete Ito Formula and Applications

We discuss several variants of the Discrete Ito formulawhich was originally developed by J. A. D. Appleby,G.Berkolaiko and A.Rodkina. We demonstrate how thisformula can be applied in the proofs of almost sure stabilityand instability of the solutions of the stochastic differenceequations, systems of the stochastic difference equations, aswell as the Euler-Milstein discretisation of an Ito stochas-tic differential equation. We also discuss application of theDiscrete Ito formula to the optimal control problem for thestochastic difference equations.

Alexandra RodkinaUniversity of the West Indies, [email protected]

MS17

Cardiac Wave Instabilities in Tissue with Inhomo-geneous Distribution of Calcium Alternans

Despite the important role of electro-mechanical alternansin cardiac arrhythmogenesis, its molecular origin is not wellunderstood. In this talk we consider alternans associatedto instabilities in the cytosolic calcium transient. Particu-larly, we study how a malfunction of the ryanodine receptor(RyR) recovery time from inactivation may induce beat-to-beat alternations in intracellular calcium concentrationand how this could affect the stimulus propagation in in-homogeneous tissue, whose cells exhibit different calciumdynamics.

Carlos LugoDepartamento de Evolucion MolecularCentro de [email protected]

144 DS13 Abstracts

Inma R Cantalapiedra, Angelina Penaranda, EnricAlvarez-LacalleDepartament de Fisica AplicadaUniversitat Politecnica de Catalunya. [email protected], [email protected],[email protected]

Blas EchebarriaDepartamento de Fiscia Aplicada. UnviersidadPolitecnica deCatalunya (UPC). Av gregorio Maranon 44 [email protected]

MS17

Dynamically Generated Complex SpatiotemporalPatterns in Cardiac Tissue

Alternans of action potential duration has been associatedwith T-wave alternans and the development of arrhyth-mias because it produces large gradients of repolarization.However, little is known about alternans dynamics in largemammalian hearts. Using optical mapping to record elec-trical activations simultaneously from the epicardium andendocardium of large mammalian hearts, we demonstratefive novel arrhythmogenic complex spatiotemporal dynam-ics not previously observed.

Flavio M. FentonCornell [email protected]

Alessio GizziCampus Bio-Medico of [email protected]

Elizabeth M. CherryRochester Institute of TechnologySchool of Mathematical [email protected]

Stefan LutherMax Planck Institute for Dynamics and [email protected]

MS17

Mechanisms of Spatially Discordant Alternans

Spatially discordant alternans (SDA) occurs when the ac-tion potential duration (APD) of different regions of tissuealternate out-of-phase. This phenomenon is arrhythmo-genic since it induces a heterogeneous distribution of re-fractoriness which can induce wave break. In this study wepropose a novel mechanism to generate SDA which is dueto the spatial heterogeneity of calcium (Ca) cycling withincells in cardiac tissue. This mechanism is robust and islikely to underlie a wide range of experimentally observedSDA patterns.

Daisuke SatoUC [email protected]

Donald BersUC [email protected]

Yohannes ShiferawCalifornia State University

[email protected]

MS17

Reduced Order Modeling of Cardiac Dynamics andPrediction of Alternans

We developed a reduced order model to describe spatiotem-poral patterns of cardiac alternans. A statistical learningmethod based on the reduced order model was developedto predict the local spatial onset of alternans from timeseries of optical mapping data from the rabbit heart .

Xiaopeng ZhaoUniversity of [email protected]

Elena TolkachevaDepartment of Biomedical EngineeringUniversity of [email protected]

MS18

Parameterization Methods for Computing Nor-mally Hyperbolic Invariant Tori

We explain numerical algorithms for the computation ofnormally hyperbolic invariant manifolds and their invariantbundles, using the parameterization method. The frame-work leads to solving invariance equations, for which oneuses a Newton method adapted to the dynamics and thegeometry of the invariant manifolds. We illustrate the algo-rithms with several examples. The algorithms are inspiredin current work with A. Haro and R. de la Llave.

Marta CanadellUniversitat de [email protected]

Alex HaroDept. of Mat. Apl. i AnalisiUniv. de [email protected]

MS18

Trajectory Design in the Spatial Circular Re-stricted Three-Body Problem using Higher-Dimensional Poincare Maps

The Circular Restricted Three-Body Problem (CR3BP)serves as a useful framework for preliminary trajectory de-sign in a multi-body force environment; however, trajec-tory design, even in this simplified dynamical regime, isoften nontrivial. The Poincare map is a powerful tool thatreduces the dimension of the problem and provides invalu-able insight into the solution space. In the spatial problem,Poincare maps must represent at least four states and aretherefore challenging to visualize. In this investigation, amethod to represent the information in higher-dimensionalPoincare maps is explored. These map representations aredemonstrated to compute heteroclinic and homoclinic con-nections associated with libration point orbits, as well asto locate families of periodic orbits about the Moon andtransfers to these orbits in the spatial problem.

Amanda HaapalaSchool of Aeronautics and AstronauticsPurdue University

DS13 Abstracts 145

[email protected]

Kathleen C. HowellPurdue UniversityWest Lafayette, IN [email protected]

MS18

Computing Singularity-Free Paths on the Configu-ration Manifold for Closed-Chain Manipulators

In Robotics a mechanism may have singular configura-tions, for which local ”velocity control” is not possible.At a singularity the mechanism ”locks”. In order to getthe mechanism to move from one configuration to anothercontrols must be chosen in a way that these singularitiesare avoided. I will describe an algorithm for computingsingularity-free paths on the configuration manifold forClosed-Chain Manipulators. The algorithm uses higher-dimensional continuation techniques to explore the mani-fold using a type of shortest path algorithm, and barriersto avoid singularities.

Michael E. HendersonIBM ResearchTJ Watson Research [email protected]

MS18

Computing Global Manifolds in the Lorenz System

The transition from simple to chaotic dynamics in theLorenz system is organised by two global bifurcations: ahomoclinic bifurcation of the origin and a heteroclinic con-nection between the origin and a saddle periodic orbit.This talk will demonstrate how the computation of two-dimensional stable manifolds as one-parameter families oforbit segments can be employed to understand the organi-zation of phase space during this transition via preturbu-lence to the well-know chaotic Lorenz attractor.

Eusebius DoedelDept of Computer ScienceConcordia [email protected]

Bernd Krauskopf, Hinke M. OsingaUniversity of AucklandDepartment of [email protected], [email protected]

MS19

Integro-differential Equations in Epidemiology Ex-plored via Delays

The sojourn time for diseases processes, e.g., recovery orimmunity time, are often assumed to be exponentially dis-tributed resulting in ODE based models. Consideration ofmore general sojourn-time distributions results in integro-differential equations (IDEs). We study IDEs as perbur-bations of ODEs or delay-differential equations. We useasymptotic methods and bifurcation theory developed forthese latter problems to understand how the properties ofthe more general sojourn-time distributions affect the sta-bilty and properties of the IDE system dynamics.

Thomas W. CarrSouthern Methodist University

Department of [email protected]

MS19

Networks with Multiple Connection Delays: Dy-namical Properties, Scaling bBhaviour and Syn-chronisation Patterns

The dynamics of networks with delayed interactions havereceived much interest, as coupling delays play an impor-tant role in diverse systems as population dynamics, traffic,communication networks, genetic circuits, and the brain.In general the different interaction delays in a network arenot equal, or may even differ by several orders of magni-tude. Here, we consider a network of networks of chaoticunits: the coupling delay within a subnetwork is muchshorter than the delay between the subnetworks. We showthat the spectrum of Lyapunov exponents has a hierarchi-cal structure, with different parts of the spectrum scalingwith the different delays. From the scaling properties of themaximal Lyapunov exponent, we can deduce the synchro-nisation properties of the network: units within a subnet-work can synchronise if the maximal exponent scales withthe shorter delay, synchronisation between different sub-networks is only possible if the maximal exponent scaleswith the long delay.

Otti D’Huys

Department of Physics (DNTK)Vrije Universiteit Brussel, [email protected]

Steffen Zeeb, Sven Heiligenthal, Thomas JuenglingInstitute for theoretical physicsUniversity of [email protected],[email protected],[email protected]

Wolfgang KinzelUniversity of Wuerzburg, [email protected]

Serhiy YanchukHumboldt University [email protected]

MS19

Delay- and Coupling-Induced Firing Patterns inOscillatory Neural Loops

We investigate the emergence of stable spiking patterns infeed-forward loops of interacting neurons which are genericcomponents of nervous systems. We show that such neuralnetworks may possess a multitude of stable spiking pat-terns and provide explicit conditions for the communica-tion delays and/or synaptic weights resulting in a desiredpattern. It can be obtained by a modulation of the coexist-ing stable in-phase synchronized states or traveling wavespropagating along or against the direction of coupling inthe homogeneous network. We also show that the delaysdirectly affect the time differences between spikes of inter-acting neurons, and the synaptic weights control the phasedifferences.

Oleksandr PopovychInstitute of Neuroscience and Medicine -Neuromodulation

146 DS13 Abstracts

Research Center Juelich, [email protected]

Serhiy YanchukInstitute of Mathematics,Humboldt University of Berlin, [email protected]

Peter A. TassInstitute of Medicine (MEG)Research Centre [email protected]

MS19

Control of Desynchronization Transitions by theBalance of Excitatory and Inhibitory Coupling inDelay-Coupled Networks

We discuss multiple synchronization and desynchronizationtransitions in networks of delay-coupled excitable systems,which arise due to a change of the ratio of excitatory andinhibitory couplings. We use a generic model of type-I ex-citability for the local dynamics of the nodes. Utilising themethod of the master stability function, we investigate thestability of the zero-lag synchronous dynamics and its de-pendence on coupling strength, delay time, and the relativenumber of inhibitory links.

Eckehard SchollTechnische Universitat BerlinInstitut fur Theoretische [email protected]

MS20

Extreme Events in Networks of Excitable Units

We investigate networks of excitable FitzHugh–Nagumounits that are capable of self-generating and -terminatingextreme events at irregular times and without employingparameter changes, external input or stochasticity. We dis-cuss dynamical properties and mechanisms that may beresponsible for the generation and termination of these ex-treme events.

Gerrit Ansmann, Klaus LehnertzDepartment of EpileptologyUniversity of Bonn, [email protected], [email protected]

MS20

The Dynamics of Two Coupled Excitable Units

Networks of excitable elements of FitzHugh Nagumo typeexhibit high amplitude events which are recurrent on largetime scales. To understand the mechanism of the genera-tion of such events, we study two diffusively coupled, non-identical FitzHugh Nagumo models. These rare spikes arefound for a parameter range where the system is chaotic.This chaotic dynamics consists of small subthreshold os-cillations with irregular spikes immersed. Possible mech-anisms behind this ”extreme” behavior of the system arediscussed.

Rajat Karnatak

Theoretical Physics/Complex Systems, ICBMUniversity [email protected]

Ulrike FeudelUniversity of OldenburgICBM, Theoretical Physics/Complex [email protected]

MS20

Detecting Precursors of Bursting Dynamics in Sim-plified Neuronal Networks

Spiking dynamics of simplified neuronal networks exhibitscomplex patterns with transitions in and out synchronousbursting. We use integrate-and-fire networks with complextopologies to investigate dynamical precursors of transi-tions in and out of the bursting on the level of correlationsof cellular groups. We compare spontaneous and evokeddynamics for excitatory only and mixed excitatory-and-inhibitory networks. We show distance dependent clus-ter formation and progressive homogeneity in neuronal dy-namics just before the transition to synchronous bursting.These results may provide insights on dynamical correlatesof seizure seizure onset in epileptic networks.

Michal ZochowskiDepartment of Physics and Biophysics ProgramUniversity of [email protected]

MS21

Reduced Model of Internal Waves


Roberto CamassaUniversity of North [email protected]

MS21

Internal Waves in the Ocean: Theoretical Perspec-tive


Yuri V. LvovRensselaer Polytechnic [email protected]

MS21

Internal Waves: Synthesis Between Theory andObservations


Kurt [email protected]

MS21

Hamiltonian Formalism for Internal Waves andTurbulence in Stratified Flows


Benno RumpfSouthern Methodist [email protected]

DS13 Abstracts 147

MS22

From Bearings to Biscuits, Practical Applicationsof Nonsmooth Dynamics


Chris BuddDept. of Mathematical SciencesUniversity of Bath, [email protected]

MS22

Sustained Oscillations in a Nonsmooth IdealizedOcean Circulation Models

Stommel developed a model which captures the basic dy-namics of thermohaline circulation but the model settlesinto a fixed mode of circulation under constant forcing.Saha modified a model by Colin de Verdiere which exhibitsoscillations in the strength of the circulation, however themodel is analytically intractable. Changes in circulationare a possible trigger to rapid climate fluctuations known asDansgaard-Oeschger events. The goal is to determine min-imal conditions under which an ocean box model exhibitsthis qualitative behavior, and geometric singular perturba-tion theory is used to do so.

Andrew RobertsDepartment of MathematicsThe University of North Carolina at Chapel [email protected]

MS22

Regularization and Singular Perturbation Tech-niques for Nonsmooth Systems

The purpose of this talk is to present some aspects of thequalitative-geometric theory of nonsmooth dynamical sys-tems. We present a survey of the state of the art on the con-nection between the regularization process of non-smoothvector fields and singular perturbation problems. We focuson exploring the local behavior of systems around typicalsingularities.

Marco TeixeiraDepartamento de MatematicaUniversidade Estadual de Campinas, [email protected]

MS22

Dynamics of a Fast Slow Piecewise Smooth Con-ceptual Climate Model

A recent augmentation of Earth’s temperature profilemodel includes a coupling with an ice line and a greenhouse effect. The model could be reduced further to a twodimensional fast slow system on a subset of the plane. Theresulting system is piecewise smooth with switches on theboundary. In this talk, I will briefly introduce a hybriddynamical system arises from this climate model, discussthe wellposedness of the system and summarize the mostrecent advances on the stability analysis.

Esther WidiasihDepartment of MathematicsThe University of [email protected]

Anna M. Barry

Institute for Mathematics and its ApplicationsUniversity of [email protected]

MS23

Bifurcations in Symmetrically Coupled Devices

I will give an overview of recent bifurcation results inmodels of symmetrically coupled devices (lasers and gy-roscopes). The lasers are delay-coupled and bifurcationsare from a rotating wave. I will present some symmetry-breaking steady-state and Hopf bifurcations from the ro-tating wave. The symmetrically coupled network of gyro-scopes has Hamiltonian structure and I will show how thebifurcation results persist under time-dependent and dis-sipative perturbations. This is joint work with J. Collera(lasers), A. Palacios and B. Chan (gyroscopes).

Pietro-Luciano BuonoUniversity of Ontario Institute of TechnologyOshawa, Ontario [email protected]

MS23

Synchrony in Coupled Cell Networks

Coupled cell systems (CCS) are systems of ordinary differ-ential equations associated with a network architecture –a finite set of nodes or cells and a finite number of arrows,representing individual dynamics and the interactions be-tween the individuals, respectively. The network structureforces the existence of certain flow-invariant subspaces, de-fined in terms of equalities of certain cell coordinates (thesynchrony subspaces) for all the associated CCS. We showhow to obtain the lattice of synchrony subspaces of a net-work based on the eigenvalue structure of the network adja-cency matrices and we present an algorithm that generatesthe lattice.

Manuela A. AguiarFaculdade de EconomiaUniversidade do [email protected]

Ana Paula S. DiasUniversidade do [email protected]

MS23

Dynamics on Asynchronous Networks

For dynamicists, a network consists of interconnected dy-namical systems (or ”nodes”). Classical networks encoun-tered in dynamics are synchronous: nodes all run on thesame clock and connectivity is fixed. Biological networks,computer networks and distributed systems generally areasynchronous: nodes may run on different clocks, connec-tivity may vary in time and nodes may stop and start run-ning. In this talk we describe and illustrate recent resultsabout dynamics on asynchronous networks.

Mike FieldRice University [email protected]

MS24

Collaborative Tracking of Coherent Structures in

148 DS13 Abstracts

Flows by Robot Teams

Tracking Lagrangian coherent structures in dynamical sys-tems is important for many applications such as oceanog-raphy and weather prediction. We present a collabora-tive robotic control strategy designed to track Lagrangiancoherent structures without requiring global informationabout the dynamics. The collaborative tracking strategyis implemented on a team of three robots and relies solelyon local sensing, prediction, and correction. We presentsimulation and experimental results and discuss theoreti-cal guarantees of the collaborative tracking strategy.

M. Ani HsiehDrexel [email protected]

Eric ForgostonMontclair State UniversityDepartment of Mathematical [email protected]

Matthew MichiniDrexel [email protected]


MS24

Lagrangian and Eulerian Indicators in a Model ofthe Chesapeake Bay

Numerical simulations and analysis of the Chesapeake Baywill be the focus of this presentation. Data from ROMS(Regional Ocean Model), specially modified for the Bay’sbathymetry, geometry, and wind forcing, is analyzed. Wewill discuss the challenges associated with interpolating thedata to acquire a velocity field to which we apply recenttools from dynamical systems to study the behavior of tra-jectories, transport and mixing, and coherence of struc-tures. Our goal is to apply Lagrangian as well as Euleriantools and indicators and discuss the strengths and weak-nesses of each technique in the context of the ChesapeakeBay.

Reza Malek-MadaniUS Naval AcademyDepartment of [email protected]

Kevin McIlhanyUnited States Naval [email protected]

Kayo IdeDept. of Atmospheric and Oceanic SciencesUniversity of Maryland, College [email protected]

Bin ZhangUniversity of [email protected]

MS24

LCS Based Detection of Key Ocean Transport Bar-

riers: Advances and Applications

The detection of transport barriers in fluid flows has widespread application, one example being the ability to im-prove predictions of the transport of pollution and debrisin the ocean, which has been become a globally importanttopic over the past few years. For this purpose, we providean overview of the LCS-based methodolgy for detecting keytransport barriers within two-dimensional flows, describingsome mathematical and practical improvements to existingmethods. To demonstrate the utility of the approach, weapply this procedure to several different case real-worldstudies.

Thomas PeacockMassachusetts Institute of [email protected]

Michael AllshouseDept. of Mechanical EngineeringMassachusetts Institute of [email protected]

C.J. [email protected]



M. Josefina OlascoagaUniversity of [email protected]

MS24

Lagrangian Data Assimilation Within the Ocean:Subsurface Observations and Three DimensionalModels

A simple kinematic model of a wind-forced three dimen-sional ocean eddy can illuminate complex dynamics of thefluid flow. However, a kinematic model alone cannot hopeto perfectly describe reality or the data one may collect.As such we propose modeling the difference between thekinematic model and data as a random function which werefer to as a bias. Once the random function is fit, weuse the now bias-corrected kinematic model to explore theeddy dynamics.

Elaine SpillerMarquette [email protected]

MS25

Rigorous Continuation of Solutions of Infinite Di-mensional Nonlinear Problems

We present a rigorous numerical method to compute globalsmooth manifolds of solutions of infinite dimensional non-linear problems. We use a parameter continuation methodon a finite dimensional projection to construct a simplicialapproximation of the manifold. This simplicial approxima-

DS13 Abstracts 149

tion is then used to construct local charts and an atlas ofthe global manifold in the infinite dimensional space. Theidea behind the construction of the smooth charts is to usethe so-called radii polynomials to verify the hypotheses ofthe uniform contraction principle on each simplex. Theconstruction of the manifold is then finalized by provingsmoothness along the common lower dimensional faces ofadjacent simplices. The method is applied to compute one-and two-dimensional bifurcation manifold of equilibria andtime periodic orbits for PDEs.

Marcio GameiroUniversity of Sao [email protected]

MS25

Rigorous Computation of Connecting Orbits inHigher Dimensions


Jason Mireles JamesRutgers [email protected]

MS25

Rigorous Numerics for Nonlinear ODEs UsingChebyshev Series

We propose a rigorous numerical method to validate solu-tions of initial and boundary value problems for nonlinearODEs. Our approach is based on the notion of Chebyshevexpansions, an analogue of Fourier series for nonperiodicproblems. We derive an equivalent problem on the infinitedimensional space of Chebyshev coefficents and computerigorous error bounds for solutions to this problem. Themethod is illustrated with an application to connecting or-bit problems in the Gray Scott System.

Christian ReinhardtTU [email protected]

Jean-Philippe LessardUniversite [email protected]

MS25

Recent Advances in Rigorous Numerics for Peri-odic and Connecting Orbits

The past few decades have seen enormous advances in thedevelopment of computer assisted proofs in dynamics. Forfinite dimensional systems there have been stunning re-sults. Attention is now turning to infinite dimensionalnonlinear dynamics generated by PDEs, integral equations,delay equations, and infinite dimensional maps. In this talkwe will review recent developments, such as the use Cheby-shev polynomials to attack connecting orbit problems, aswell as applications in the setting of spatio-temporal peri-odicity.

Jan Bouwe Van Den BergVU University AmsterdamDepartment of [email protected]

MS26

An Iterative Method for the Canard Explosion inGeneral Planar Systems

The canard explosion is the change of amplitude of a limitcycle in a narrow parameter interval. It is well understoodin singular perturbation problems where a small parametercontrols the slow/fast dynamics but also occurs in systemswith no explicit small parameter. We show how the iter-ative method of Roussel and Fraser, devised to constructregular slow manifolds, can be used to determine a canardpoint in a general planar system.

Morten BronsTech University of DenmarkDepartment of [email protected]

MS26

Inflection Methods for Singular Perturbation Prob-lems

Inflection methods for dynamical systems rely on comput-ing (analytically and/or numerically) the locus of pointsin the phase space where a solution curve has zero localcurvature. In problems with multiple time scales, partsof these inflection sets approximate slow manifolds and, inthe neuronal context, offer a tractable access to excitabilitythresholds. In this talk, I will review inflection techniquesfor slow-fast dynamical systems and present recent resultson canards in ε-free systems investigated using these tech-niques.

Mathieu DesrochesINRIA [email protected]

Martin KrupaINRIA [email protected]

Serafim RodriguesPlymouth University (UK)[email protected]

MS26

An Iterative Approach for the Computation of Ca-nards and their Transients

The computation of canards in slow-fast systems using col-location methods is potentially hampered by the fact thatthe computational complexity increases with decreasing ep-silon. Here we suggest a different approach that circum-vents this issue. It is based on iterative methods for thecomputation of the slow manifold and approximations tothe fiber projections that allow for a splitting of the systeminto non-stiff sub-systems. We present some convergenceestimates and numerical results.

Kristian U. KristiansenDepartment of MathmaticsTechnical University of [email protected]

MS26

Algorithmic Multiscale Reduction: Analysis, Chal-

150 DS13 Abstracts

lenges, Hits and Misses

Nonlinear multiscale reduction methods originated in theapplied sciences a century ago. Their mathematical for-malization proved invaluable but riddled them with anε 1, whose explicit identification is problematic for com-plex models. I will first present methods understandablewithin a simple differential geometric framework, outliningresults and research opportunities. I will then consider aglycolysis model, show how inopportune applications of theclassic QSSA method reverse system behavior and discussQSSA robustness for large biochemical models.

Antonios ZagarisUniversiteit [email protected]

MS27

Identifiability and Parameter Estimation of Multi-ple Transmission Pathways in Disease

Waterborne diseases such as hepatitis A, cholera, and awide range of other bacterial and viral diseases cause over1.8 million deaths annually. These diseases often exhibitmultiple pathways or timescales of transmission. In thistalk I will discuss some of our recent work examining theidentifiability, parameter estimation and dynamics of mul-tiple transmission pathways in disease, including initialwork examining how the structure of networks of connec-tivity for human and water movement affect disease dy-namics.

Marisa EisenbergUniversity of [email protected]

MS27

Mathematical Model of Infection by Genetically-Engineered Viruses to Induce An Anti-Cancer Im-mune Response

A new strategy for cancer treatment relies on usinggenetically-engineered viruses to infect and kill tumorcells and potentially induce an anti-tumor immune re-sponse. Recent experiments with engineered adenovirushave caused substantial reduction in growth rates of tumorsin mice; however, the tumors always relapse. By fittingtime series data to mathematical models, we attempt toelucidate underlying cancer-virus and cancer-immune dy-namics and propose improved methods of treatment.

Peter S. KimUniversity of SydneySchool of Mathematics and [email protected]

Joseph J. CrivelliWeill Cornell Medical [email protected]

Joanna WaresUniversity of RichmondDepartment of Mathematics and Computer [email protected]

MS27

The Impact of Vaccination and Transgenic

Mosquitoes on the Evolution of the Dengue Virus

Dengue is a mosquito-borne viral pathogen that causeslarge amounts of disease in the tropics and sub-tropics.Two new interventions for dengue are currently in in-tense development: a vaccine that protects against all fourserotypes and transgenic mosquitoes that are less-suitablevectors. We developed a mathematical model for evolutionof dengue viruses in response to these new interventions. Iwill discuss results from the model, including interventionsthat would pose the least risk of selecting for more virulentdengue strains.

Jan MedlockOregon State [email protected]

MS27

A Perspective on Multiple Waves of Influenza Pan-demics

A striking characteristic of the past four influenza pan-demic outbreaks in the United States has been the multiplewaves of infections. However, the mechanisms responsiblefor these waves are uncertain. In this talk several distinctmechanisms are exhibited each of which can generate twowaves of infections for an acute infectious disease. Each isincorporated into a susceptible-exposed-infected-removedmodel. The models are used to examine the effects of bor-der control and vaccination.

Anna MummertMarshall [email protected]

Howard WeissGeorgia [email protected]

Li-Ping LongMississippi State [email protected]

Jose M. AmigoCentro de Investigacion [email protected]

Xiu-Feng WanMississippi State [email protected]

MS28

Effects of Reduced Discrete Coupling on FilamentTension in Excitable Media

Wave propagation in the heart is mediated by discrete in-tercellular connections via gap junctions. Effects of dis-creteness on waves in two and three dimensions are ex-plored. We study the effect of discrete cell coupling onthe filament dynamics in a generic model of an excitablemedium. We find that reduced cell coupling decreases theline tension of scroll wave filaments and may induce neg-ative filament tension instability in three-dimensional ex-citable lattices.

Sergio AlonsoPhysikalisch-Technische BundesanstaltBerlin, [email protected]

DS13 Abstracts 151

MS28

Dynamics of Scroll Filaments, and Buckling ofScrolls in Thin Media

Scroll wave turbulence occurs in excitable media with neg-ative filament tension. In a thin layer, a scroll can be sta-bilized by “filament rigidity’. Above a critical thickness,scroll deforms into a buckled, precessing state. On the sur-face this is seen as spiral wave meandering, the amplitudeof which grows with the layer thickness, until a break-up tothe scroll turbulence happens. We present a simplified the-ory for this phenomenon and illustrate it with numericalexamples.

Hans DierckxDepartment of Physics and AstronomyGhent [email protected]

Henri VerscheldeGhent [email protected]

Ozgur SelsilUniversity of [email protected]

Vadim N. BiktashevCollege of Engineering, Mathematics and PhysicalSciencesUniversity of [email protected]

MS28

Low-energy Control of Electrical Turbulence in theHeart

Control of complex spatio-temporal dynamics underlyinglife-threatening cardiac arrhythmias is difficult, because ofthe nonlinear interaction of excitation waves in a hetero-geneous anatomical substrate. We show that in responseto a pulsed electric field, heterogeneities related to coro-nary vascular structure serve as nucleation sites for intra-mural electrical waves, which allow targeting of electricalturbulence near the cores of the vortices of electrical activ-ity. Using this control strategy, we demonstrate low-energytermination of fibrillation in vivo.


MS28

Filament Interaction and Self-Wrapping Filamentsin An Excitable Reaction System

The three-dimensional Belousov-Zhabotinsky reaction self-organizes scroll waves that rotate around one-dimensionalphase singularities called filaments. These filaments movewith speeds proportional to their local curvature and fil-ament loops shrink and annihilate in finite time (positivefilament tension). Local pinning of the filament can af-fect this process and induce stable vortex patterns. Inthis talk I will discuss recent results on the pinning offilament loops to small unexcitable heterogeneities. Suchconfigurations allow the investigation of filament interac-tion. In addition, I will present results on the self-wrappingof filaments around unexcitable cylinders with radii muchsmaller than the vortex wavelength. This self-wrapping re-

shapes the rotation backbone and wave field of the vortexprofoundly. The relevance of these findings for cardiologyare discussed. All experimental results are complementedby numerical simulations with a piece-wise linear reaction-diffusion model.

Oliver SteinbockDepartment of Chemistry and BiochemistryFlorida State [email protected]

MS29

Particle Size Segregation and Spontaneous LeveeFormation in Geophysical Mass Flows

Hazardous geophysical mass flows, such as debris flows, py-roclastic flows and snow avalanches, often develop coarseparticle rich levees that channelize the flow and enhancerun-out. They are formed by large particles rising to thesurface and being preferentially transported to the flowfront, where they experience greater resistance to motionand are shouldered aside. A first attempt at modellingsuch segregation-mobility feedback effects is made usingdepth-averaged models.

Nico GraySchool of Math., Univ. of Manchester,Oxford Rd., Manchester M13 9PL, UK, Tel: +44(0) 161275 [email protected]

James BakerThe University of Manchestern/a

MS29

Analysis of a Dynamical Systems Model for Gran-ular Flow

We describe an infinite-dimensional dynamical system (theBSR model) devised to study granular flows, but which hasalso proven effective in predicting general material interac-tion phenomena. After briefly treating the well-posednessof this system, we prove it is Hamiltonian for certain per-fectly elastic interactions and present results on completeintegrability. Finally, we show that the system can be re-duced, in an approximate sense, to a finite-dimensional dis-crete dynamical system that yields information on chaotictransitions.

Denis BlackmoreNew Jersey Institute of TechnologyNewark, NJ 07102, [email protected]

Anthony RosatoNew Jersey Institute of TechnologyNewark, NJ 07102, [email protected]

Xavier M. TricochePurdue UniversityWest Lafayette, IN [email protected]

Hao WuNew Jersey Institute of TechnologyNewark, NJ 07102 [email protected]

152 DS13 Abstracts

Kevin UrbanNew Jersey Institute of TechnologyNewark, NJ [email protected]

MS29

Important Time Scales in the Dynamics of Granu-lar Material

The state of granular media can be represented by a persis-tence diagram. This representation provides an interestinginsight into the physical properties of the granular media asdemonstrated on a system undergoing compression. Timeevolution of the system can be seen as a curve in the spaceof persistence diagrams. Different notions of distance inthis space provide a useful tool for understanding the dy-namic. In particular the compressed systems (viewed as adiscrete dynamical system) exhibit a few different regimeswhere dynamics changes from fast to slow. Dependenceof the system on its previous state is strongly affected bythe sampling rate. We conclude the talk by addressing theproblem of determining the ’appropriate’ sampling rate.

Miroslav KramarRutgers UniversityDepartment of [email protected]

Konstantin MischaikowDepartment of MathematicsRutgers, The State University of New [email protected]

Lou KondicDepartment of Mathematical Sciences, NJITUniversity Heights, Newark, NJ [email protected]

Arnaud [email protected]

MS29

Mixing by Cutting and Shuffling in 3D GranularFlow

We study chaotic dynamics of granular flow in a sphericaltumbler rotating alternately about two orthogonal axes inthe limit of an infinitely thin flowing layer. Mixing occursthrough cutting and shuffling, is sensitive to the combina-tion of rotation angles about each axis and can be reducedto dynamics on a hemispherical shell (2D). Poincare mapson this shell show patterns that include elliptic regionsreminiscent of partitions generated by piecewise isometries(PWI).

Paul UmbanhowarNorthwestern UniversityEvanston, IL [email protected]

Paul ParkNorthwestern [email protected]

Richard M. LueptowNorthwestern UniversityDepartment of Mechanical Engineering

[email protected]

Julio OttinoNorthwestern UniversityEvanston, IL [email protected]

MS30

Network Structure and Predictive Dynamics ofBrain Systems

The human brain is a network of cortical areas connectedby structural or functional highways along which informa-tion propagates. Using non-invasive neuroimaging data, weshow that brain network structure varies both over timeand between individuals. We identify dynamic networkproperties that predict individual differences in cognitivebehaviors such as learning. These results inform statisticalapproaches to predict individual brain responses to clinicalinterventions, potentially enabling personalized monitoringof disease progression and rehabilitation.

Danielle S. Bassett, Nicholas F. WymbsUniversity of California Santa [email protected], [email protected]

Mason A. PorterUniversity of [email protected]

Peter J. MuchaUniversity of North Carolina Chapel [email protected]

Jean M. Carlson, Scott T. GraftonUniversity of California Santa [email protected], [email protected]

MS30

Geometric Network Models of the Functional Con-nectome

Null network models, such as Erdos Renyi random graphsor random graphs with fixed degree distributions providea foundation for modern network analyses, both in the de-sign and evaluation of network metrics. In this talk wedescribe a class of null models which capture both geom-etry and degree distribution, while maintaining analytictractability, and discuss several applications to the analy-sis of functional connectomes.

Eric FriedmanCornell [email protected]

Adam LandsbergJoint Sciences, the Claremont [email protected]

MS30

Statistical Aspects of Diffusion Fiber Tracking


Roland HenryDepartment of NeurologyUCSF School of [email protected]

DS13 Abstracts 153

MS30

A Linear Model Based on Network Diffusion Pre-dicts Functional Correlation Networks in the Brainfrom Structural Connectivity Networks


Ashish [email protected]

MS31

Exploiting Numerical Diffusion to Study Transportand Chaotic Mixing

In this talk I will demonstrate that the purely convectivemapping matrix approach provides an extremely versatiletool to study advection-diffusion processes for extremelylarge Peclet values. This is made possible due to the coarse-grained approximation that introduces numerical diffusion,the intensity of which depends in a simple way on grid res-olution. This observation permits to address fundamentalphysical issues associated with chaotic mixing in the pres-ence of diffusion. Specifically, we show that in partiallychaotic flows, the dominant decay exponent of the advec-tion diffusion propagator will eventually decay as Pe to thepower -1 in the presence of quasiperiodic regions of finitemeasure, no matter how small they are. Examples of 2dand 3d partially chaotic flows are discussed.

Patrick AndersonEindhoven University of [email protected]

MS31

Global Stability Design of Autonomous Time-continuous Systems

Given a stable non-linear system, one would like to com-pute its stability region. Often, the system depends onparameters, which should be tuned to shape this regionaccording to one’s needs. More generally, one would liketo perform an efficient quantitative study of the global sta-ble behavior of the system; and to optimize this. In thistalk I introduce a fairly general framework for doing thatby approximating the deterministic dynamics via a finitedimensional stochastic process. Translating the desired ob-jectives in the terms of this process yields a simple compu-tation and also the application of optimization algorithms.The probabilistic nature of the approximation enables anunderstanding beyond that what standard numerical anal-ysis can offer. In particular, no trajectory simulation isneeded during the computation. The main advantage ofthe method lies in the resulting numerical efficiency andthe general applicability for a wide range of objectives.

Peter KoltaiCenter for MathematicsMunich University of Technology, [email protected]

MS31

Transfer Operator Based Numerical Methods forAnalysing Coherent Structures in Time-dependentSystems

After a short review of recent developments in transfer op-erator methods for studying finite-time transport, we willintroduce a modified construction for characterizing La-

grangian coherent sets in nonautonomous dynamical sys-tems. This approach takes into account both future andpast information on the dynamics and is suited to track-ing coherent sets over several finite-time intervals. We willexplore in example systems how diffusion and finite-timeduration influence the structures of interest.

Kathrin Padberg-GehleInstitute of Scientific ComputingTU [email protected]


MS31

Identifying Topological Chaos Using Set-orientedMethods

The transfer operator eigenspectrum for a dynamical sys-tem can identify sets in (phase) space that remain nearlyinvariant (by some appropriate definition). A continuous,non-autonomous dynamical system such as a fluid flow cancontain multiple distinct sets that move about one anotherin a non-trivial way. The topology of the set trajecto-ries enables a classification of the global flow that includesquantification of the topological entropy. Viscous fluid ex-amples will be discussed.

Mark A. StremlerVirginia [email protected]

Pradeep RaoEngineering Science & MechanicsVirginia [email protected]

MS32

Relating the Water Wave Pressure to its SurfaceElevation

A new method is proposed to recover the water-wave sur-face elevation from pressure data obtained at the bottomof the fluid. The new method requires the numerical solu-tion of a nonlocal nonlinear equation relating the pressureand the surface elevation which is obtained from the Eulerformulation of the water-wave problem without approxi-mation. From this new equation, a variety of differentasymptotic formulas are derived. The nonlocal equationand the asymptotic formulas are compared with both nu-merical data and physical experiments.

Bernard DeconinckUniversity of [email protected]

Katie OliverasSeattle UniversityMathematics [email protected]

MS32

Solitary Waves on Water and Their Stability

The talk will discuss recent development on the existenceand stability of two- and three-dimensional solitary waves

154 DS13 Abstracts

on the surface of water with finite depth using variousmodel equations or exact Euler equations. It was knownthat these equations have solitary-wave solutions and thestability of these waves in many problems is still open.Here, some stability results for these waves will be ad-dressed, such as transverse instability, conditional stabilityor asymptotic linear and spectral stability.

Shu-ming SunDept. of Math.Virginia Polytechnic Institute and State [email protected]

MS32

A Dimension-breaking Phenomenon for SteadyWater Waves with Weak Surface Tension

I will discuss the bifurcation of three-dimensional periodi-cally modulated solitary waves from two-dimensional linesolitary waves in the presence of weak surface tension. Thenew waves decay in the direction of propagation and areperiodic in the transverse direction. The proof is based onspatial-dynamics and an infinite-dimensional version of theLyapunov centre theorem. The method also reveals thatthe line solitary waves are linearly unstable to transverseperturbations.

Mark D. GrovesUniversitat des [email protected]

Shu-Ming SunVirginia TechDepartment of [email protected]

Erik WahlenLund [email protected]

MS32

Quasi-periodic Perturbations of Time-periodic Wa-ter Waves

We develop a high-performance shooting algorithm tocompute new families of time-periodic and quasi-periodicsolutions of the free-surface Euler equations involvingbreathers, traveling-standing waves, and collisions of soli-tary waves of various types. The wave amplitudes are toolarge to be well-approximated by weakly nonlinear theory,yet we often observe behavior that resembles elastic colli-sions of solitons in integrable model equations. A Floquetanalysis shows that many of the new solutions are stableto harmonic perturbations.

Jon WilkeningUC Berkeley [email protected]

MS33

The Curse of Dimensionality for the Border Colli-sion Normal Form

I will discuss the dynamics of higher dimensional bordercollision bifurcations, showing that there exist parametersfor which the n-dimensional normal form has attractorsthat cannot exist in the (n-1)-dimensional version. These

results also have implications for grazing-sliding bifurca-tions of continuous time systems. This is joint work withMike Jeffrey (University of Bristol).

Paul GlendinningUniversity of [email protected]

MS33

The Uncertainties of Nonsmooth Dynamics

A discontinuity in a set of differential equations generallyleads to infinitely many possible solutions. Why, then, hasFilippov’s ‘sliding’ solution been successful in studying ev-erything from stick-slip dynamics to electrical switching?We show that an idealized mathematical model with dis-continuities has infinitely many solutions, but that by as-suming a lack of exact knowledge of the system, Filippov’ssolution becomes valid, and one can quantify the balanceof modelling errors for which this remains true.

Mike R. JeffreyUniversity of [email protected]

MS33

Singular Dynamics in Gene Network Models

Gene regulatory networks are commonly modeled bysteep/step sigmoid interactions which leads to difficul-ties when the gene expressions are close to their thresh-olds. A method to analyze this situation is the frameworkbased on singular perturbation techniques. We present 3-dimensional examples that do not fit the classical singularperturbation theory. We therefore suggest a generaliza-tion of the classical singular perturbation techniques thatis based on the Artstein theory of dynamic limits of thefast flow.

Anna MachinaUniversity of [email protected]

MS33

Singular Matching Near a Visible Fold-regularPoint: Asymptotics of the Return Map

We combine geometric singular perturbation theory withmatching perturbation methods to study the local map ofnear-grazing solutions at the boundary between crossingand sliding dynamics, in the smoothing of a Filippov-typenonsmooth dynamical system. We show that the Lipchitzconstant is of order O(εα), α > 0, in terms of the singularperturbation parameter ε. The value of α depends on thesmoothness of the function regularizing the discontinuity.The persistence of periodic orbits is discussed.

Tere M. SearaUniv. Politecnica de [email protected]

Carles BonetUniversitat Politecnica de [email protected]

MS34

Linearization Theorems and Koopman Operator

DS13 Abstracts 155

Spectrum

The spectrum of Koopman operator describes the changeof distributions in the phase space and is crucial for aglobal analysis of system properties from a measure the-oretic point of view. We present a new way of analyzingthis spectrum based on linearization of nonlinear systemsin its basin of attraction.

Yueheng LanTsinghua [email protected]

MS34

Isochrons and Isostables of Dynamical Systems:Relationship to Koopman Operator Spectrum

The spectral properties of the Koopman operator are re-lated to the well-known isochrons of limit cycles. Thisobservation yields an efficient method to compute theisochrons in high-dimensional spaces and provides a newperspective to extend this notion to nonperiodic systems(e.g. quasiperiodic tori). For a stable fixed point, theisochrons are defined through the same framework andcomplemented with the so-called isostables required for the(action-angle) reduction of the dynamics.

Alexandre Mauroy, Igor MezicUniversity of California, Santa [email protected], [email protected]

MS34

Koopman Operator Methods: An Overview

Koopman (or composition) operator is a linear infinite-dimensional operator that can be defined for any nonlineardynamical system. The linear operator retains the full in-formation of the nonlinear state-space dynamics. The for-malism based on Koopman operator representation holdspromise for extension of dynamical systems methods to sys-tems in high-dimensional spaces as well as hybrid systems,with a mix of smooth and discontinuous dynamics. Re-cently, Koopman operator properties have been intenselystudied, and applications pursued in fields as diverse asfluid mechanics and power grid dynamics. We will overviewthe current status of Koopman operator methods in dy-namical systems and their applications.


MS34

Koopman Operator Methods in Fluid Mechanics

We study coherent structures in fluid flows using analysisof the Koopman operator. Given a vector of observablesfor a dynamical system (for instance, flow information ina particular region of space), one may determine a corre-sponding set of “Koopman modes,” which are the coeffi-cients in an expansion in Koopman eigenfunctions. Thesemodes may be extracted from data using Dynamic ModeDecomposition, a variant of the Arnoldi algorithm, andelucidate coherent structures in the flow.

Clarence RowleyPrinceton UniversityDepartment of Mechanical and Aerospace [email protected]

MS35

Approximate Deconvolution Large Eddy Simula-tion of the Quasi-Geostrophic Equations of theOcean

This talk introduces a new approximate deconvolution clo-sure modeling strategy for the quasi-geostrophic equationsmodeling the large scale oceanic flows. The new large eddysimulation model is successfully tested in the numericalsimulation of the wind-driven circulation in a shallow oceanbasin, a standard prototype of more realistic ocean dynam-ics. This first step in the numerical assessment of the newmodel shows that approximate deconvolution could repre-sent a viable alternative to standard eddy viscosity param-eterizations in the large eddy simulation of more realisticturbulent geophysical flows.

Traian IliescuDepartment of MathematicsVirginia [email protected]

MS35

Approximate Deconvolution Models for LES of At-mospheric Boundary Layer Flows

Atmospheric boundary layer flows exhibit a range of turbu-lent conditions over the course of a diurnal cycle. Our in-terest is in approximate deconvolution method algorithmsfor subfilter-scale closures in large-eddy simulation to bet-ter represent intermittent turbulence and to facilitate flowtransitions across mesh refinement boundaries. The ex-plicit filtering and reconstruction approach allows genera-tion of intermittent turbulence even under strong nighttimestratification and improves representation of appropriatescales as the flow transitions across grid nesting interfaces.

Tina Katopodes ChowDepartment of Civil and Environmental EngineeringUniversity of California, Berkeley, [email protected]

Lauren GoodfriendUC [email protected]

Bowen ZhouDepartment of Civil and Environmental EngineeringUniversity of California, Berkeley, [email protected]

MS35

Modeling Error in Approximate DeconvolutionModels

We investigate the asymptotic behaviour of the modelingerror in approximate deconvolution model in the 3D peri-odic case, when the order N of deconvolution goes to in-finity. We consider successively the generalised Helmholzfilters of order p and the Gaussian filter. For Helmholz fil-ters, we estimate the rate of convergence to zero thanks toenergy budgets, Gronwall’s Lemma and sharp inequalitiesabout Fouriers coefficients of the residual stress. We nextshow why the same analysis does not allow to concludeconvergence to zero of the error modeling in the case ofGaussian filter, leaving open issues.

Roger Lewandowski

156 DS13 Abstracts

IRMAR, UMR 6625Universite Rennes [email protected]

MS35

Unconditionally Stable and Optimally AccurateTimestepping Methods for Approximate Deconvo-lution Models

We address an open question of how to devise numericalschemes for approximate deconvolution models that are ef-ficient, unconditionally stable, and optimally accurate. Wepropose, analyze and test a scheme for these models thathas each of these properties. There are several importantcomponents to the derivation, both at the continuous anddiscrete levels, which allow for these properties to hold.The proofs of unconditional stability and optimal conver-gence are carried out through the use of a special choiceof test function and some technical estimates. Numericaltests are also provided.

Leo RebholzClemson UniversityDepartment of Mathematical [email protected]

MS36

Response of the Sea Ice Seasonal Cycle to ClimateChange

The Northern Hemisphere sea ice cover has diminishedrapidly in recent years and is projected to continue to di-minish in the future. The year-to-year retreat is faster insummer than winter, which has been identified as one ofthe most striking features of satellite observations as wellas of IPCC model projections. This is typically understoodto imply that the sea ice cover is most sensitive to climateforcing in summertime. However, in the Southern Hemi-sphere it is the wintertime sea ice cover that retreats fastestin IPCC model projections. Here, we address the seasonalstructure of observed and simulated sea ice retreat in bothhemispheres. We propose a physical theory that primarilyinvolves the shape of coastlines and eddy heat fluxes in theatmosphere. We demonstrate that the theory accuratelydescribes a wide range of climates simulated with a hierar-chy of models ranging from an idealized ffatmosphere-seaice model to a state-of-the-art coupled GCM.

Ian EisenmanScripps Institution of [email protected]

MS36

Multiple Sea Ice States and Hysteresis in Simpleand Complex Climate Models: Why the OceansMatter

Sea ice exerts a positive radiative feedback which can giverise to multiple equilibria and hysteresis in the climatesystem. Climate simulations with a coupled atmosphere-ocean-sea ice general circulation model that permit at leastfour different stable states ranging from warm ice-free con-ditions to 100% ice cover, all of which are consistent withpresent-day greenhouse gas and solar radiation. The inter-action between sea ice and ocean heat transport provideskey constraints on the number and type of possible equi-libria, as well as governing many aspects of the transientadjustment between stable states. I will discuss how this

interaction is misrepresented in many simple climate mod-els, and how to fix it. Finally I will discuss implications ofmultiple equilibria in past climate change, including Snow-ball Earth and the last ice age.

Brian RoseDept of Atmospheric Sciences, University of WashingtonBox 351640, Seattle, WA [email protected]

MS36

Reversibility of Arctic Sea Ice Retreat - A Concep-tual Multi-scale Modeling Approach

A lattice-type thermodynamic complex systems model forthe ice-albedo feedback is introduced that includes the ba-sic physics of ice-water phase transition, a nonlinear diffu-sive energy transport in a possibly heterogeneous ice-oceanlayer, and spatiotemporal atmospheric and oceanic drives.At the local scale the model reveals bistability in sea iceloss. At the regional scale, however, hysteresis in sea iceretreat is structurally not stable.

Renate A. WackerbauerUniversity of Alaska FairbanksDepartment of [email protected]

Marc Mueller-StoffelsUniversity of AlaskaFairbanks, AK [email protected]

MS36

On the Existence of Stable Seasonally Varying Arc-tic Sea Ice in Simple Models

Within the framework of lower order thermodynamic theo-ries for the climatic evolution of Arctic sea ice we isolate theconditions required for the existence of stable seasonally-varying solutions, in which ice forms each winter and meltsaway each summer. We construct a two-season model fromthe continuously evolving theory of Eisenman and Wett-laufer (2009) and showing that seasonally-varying statesare unstable under constant annual average short-wave ra-diative forcing. However, dividing the summer season intoan ice covered and ice free interval provides sufficient free-dom to stabilize seasonal ice. The condition for stabil-ity is determined viz., when the ice vanishes in summerand hence the relative magnitudes of the summer heat fluxover the ocean versus over the ice. Finally, a new stochas-tic perturbation theory is developed for the original non-autonomous continuously varying model and its momentsare analyzed in light of observations.

John S. WettlauferDept of Physics, Geophysics, and Applied Mathematics,Yale University,[email protected]

MS37

Understanding Homoclinic Bifurcations via theComputation of Global Invariant Manifolds

In three-dimensional vector fields, if the one-dimensionalunstable manifold of a saddle equilibrium lies on its two-dimensional stable manifold, then a homoclinic orbit ex-ists. Typically, breaking the homoclinic orbit leads to a

DS13 Abstracts 157

rearrangement of these invariant manifolds and a reorga-nization of the overall dynamics in phase space. We showhow the computation of global two-dimensional invariantmanifolds helps us to understand their role as separatricesand basin boundaries near several codimension-one and -two homoclinic bifurcations.

Pablo AguirreUniversidad Tecnica Federico Santa MaraDepartamento de [email protected]


MS37

Global Bifurcations Lead to Bursting in a Two-Mode Laser

We present an unusual bursting mechanism in a two-modesemiconductor laser with single-mode optical injection. Bytuning the strength and frequency of the injected light wefind a transition from purely single-mode intensity oscilla-tions to bursting in the intensity of the uninjected mode.We explain this phenomenon on the basis of a simple two-dimensional dynamical system, and show that the burst-ing in our experiment is organised by global bifurcations oflimit cycles.

Andreas AmannSchool of Mathematical SciencesUniversity College [email protected]

Nicholas BlackbeardMathematics Research InstituteUniversity of Exeter, Exeter, [email protected]

Simon Osborne, Stephen O’BrienTyndall National InstituteUniversity College Cork, Cork, [email protected], [email protected]

MS37

Interacting Invariant Sets in a Noninvertible Pla-nar Map Model of Wild Chaos

We study a noninvertible planar map that is a model forwild Lorenz-like chaos in a five-dimensional vector field.We are concerned with the transition to wild chaos viathe interaction between the stable and unstable sets of asaddle fixed point and the critical set of the map, whichconsists of the images and preimages of the critical point.These interactions correspond to homo- and heteroclinicbifurcations in the underlying vector field.

Stefanie Hittmeyer, Bernd Krauskopf, Hinke M. OsingaUniversity of AucklandDepartment of [email protected],[email protected], [email protected]

MS37

Global Bifurcations in a Non-Invertible Model of

Asset Pricing

We introduce a canonical form for a standard model of as-set pricing. The resulting (non-invertible) two-dimensionaldynamical system depends on two parameters only, a rateof geometric decay and a mean reversion parameter. Wedetect parameter regimes for which homoclinic and hete-roclinic orbits exist and illustrate corresponding intersec-tions of stable and unstable sets. Finally, autocorrelationsof prices and returns before and after these global bifurca-tions are discussed.

Thorsten Huls, Volker BohmUniversitaet [email protected],[email protected]

MS38

The Topology of Non-Linear Global Carbon Dy-namics: From Tipping Points to Planetary Bound-aries

In this talk, I will present a minimal model of land use andcarbon cycle dynamics and explores the relationship be-tween nonlinear dynamics and planetary boundaries. Onlythe most basic interactions between land cover, terrestrialcarbon stocks and atmospheric carbon stocks are consid-ered. The goal is not to predict global carbon dynamicsas it occurs in the actual earth system, but rather, to con-struct a conceptually reasonable representation of a feed-back system between different carbon stores like that of theactual earth system and use it to explore the topology ofthe boundaries of what can be called a safe operating spacefor humans. The analysis of the model illustrates the po-tential complexity of planetary boundaries and highlightssome challenges associated with navigating them.

Marty AnderiesArizona State [email protected]

MS38

Forecasting the Truth with a Cleverly Inflated En-semble

Predictions of the future state of the Earth’s atmosphereare typically based on a collection of numerical simula-tions whose variance represents the forecast uncertainty.Inspired by techniques from shadowing theory, we developa novel method for improving forecasts during integrationof a weather model. The algorithm involves injecting arti-ficial uncertainty into the forecast, but only in directions ofstate space experiencing contraction in the form of negativelocal Lyapunov exponents.

Chris DanforthMathematics and StatisticsUniversity of [email protected]

Ross [email protected]


158 DS13 Abstracts

MS38

Dynamical Systems and Planet Earth

This overview talk will introduce the audience to variousapplications of dynamical systems in climate science. Theemphasis will be on a system-level approach, where theEarth’s climate system is viewed as a complex system andmanifestations of collective behavior are more importantthan details of the internal dynamics. Topics to be pre-sented include energy balance models, ocean circulationmodels, oscillatory networks and teleconnections, Lorenzmodels, biogeochemical processes, and the carbon cycle.

Hans G. KaperGeorgetown UniversityArgonne National [email protected]

MS38

Tipping Points: Overview and Challenges

Mathematical mechanisms for tipping points will be intro-duced, starting with the conceptual framework of bifurca-tion theory, and then highlighting some of the challengesand limitations of exploiting this framework for problemsarising in applications. Parts of the discussion will be de-veloped in the setting of case studies of possible tippingpoints in models of (1) Arctic sea-ice retreat, and (2) de-sertification.

Mary SilberNorthwestern UniversityDept. of Engineering Sciences and Applied [email protected]

MS38

Exploring the Decision-support Component ofMPE Questions

One of the ways that climate and sustainability applica-tions differ from other applications of dynamical systemsis their close connection with decision-making and policy.We will explore how a decision-support viewpoint may in-spire new dynamical questions.

Mary Lou ZeemanBowdoin CollegeDepartment of [email protected]

MS39

Ionic Dynamics Mediate Pattern Generation inEpilepsy

Many types of epileptic seizures involve repetitive periodsof tonic spiking and bursting activity. We found that thechanges of the intracellular and extracellular ion concentra-tions can have profound effects on the network dynamicsand may be responsible for the characteristic patterns ofelectrical activity observed during seizures. Our results willlikely have implications onto drug development and deepenour understanding of the origin of seizures.

Maxim BazhenovDepartment of Cell Biology and NeuroscienceUniversity of California, [email protected]

Giri Krishnan

UC [email protected]


MS39

The Impact of Network Structure on Criticality inCortical Circuits

Cortical circuits have been hypothesized to operate near acritical point for optimality. Previous evidence supportingthis came from bulk signals that did not show individualneuron activity. Using a 512 electrode array, we recordedhundreds of spiking neurons and found two main things:(1) Avalanche shapes can be collapsed onto a universalscaling function, a key indicator of criticality; (2) The net-work structure of effective connections strongly influencesthe critical exponents of the system.

John M. BeggsIndiana UniversityDept. of [email protected]

Karin DahmenUniversity of Illinois, Department of [email protected]

Lee DeVilleUniversity of Illinois, Department of [email protected]

Tom ButlerMassachusetts Institute of [email protected]

Nir FriedmanUniversity of [email protected]

Masanori ShimonoPhysics Department, Indiana [email protected]

Shinya ItoIndiana [email protected]

Braden BrinkmanUniversity of [email protected]

MS39

From Neuron Dynamics to Network Plasticity

Spatiotemporal dynamics in neural networks depends ontwo factors: dynamical properties of individual neuronsand characteristics of network connectivity. In the brain,however, these two factors vary dynamically and are in-tertwined in a highly complex way. Through simulationsof large-scale spiking neuron network models, we will dis-cuss how heterogeneity in network structure, heterogeneityin cellular excitability and plasticity of synaptic connectiv-ity interact to collectively influence network spatiotemporal

DS13 Abstracts 159

dynamics.

Michal ZochowskiDepartment of Physics and Biophysics ProgramUniversity of [email protected]

Victoria BoothUniversity of MichiganDepts of Mathematics and [email protected]

MS39

Distributed Control in Mean-field Cortical Net-work Models

Brain stimulation has been proposed to control pathologi-cal neuronal activity during seizure. Such activity can beviewed as a network event that begins with or without aclear spatial focus and spreads through a cortical network.This talk will assess distributed control, envisioned as gridsof local stimulating electrodes, in this scenario through theuse of mean-field neuronal network models. The controlefficacy as a function of topology and connection dynamicswill be shown.

ShiNung ChingWashington University in St. [email protected]

Mark KramerBoston [email protected]

MS39

Performance Limitations of Thalamic Relay: NewInsights into Thalamo-Cortical Processing, Parkin-son’s Disease and Deep Brain Stimulation

Humans have the remarkable ability to selectively processsensory information. In the motor system, we select whichmuscles to turn on and off during movement. In this talk,we describe how and when selective processing occurs in athalamic cell. We compute bounds on thalamic relay re-liability that explain observed patterns of neural activityin the basal ganglia in (i) health (ii) in Parkinsons disease(PD), and (iii) in PD during therapeutic deep brain stim-ulation.

Sridevi Sarma, Rahul AgarwalJohns Hopkins [email protected], [email protected]

MS40

Collision of a Flexible Filament with a Point Vortex

I will first review vortex methods for flows coupled to de-forming flexible filaments, which can serve as models forfish bodies, fins, and other immersed structures. I willthen focus on the attraction between a flexible filament isattracted to a point vortex when they move together as acoupled system. The point vortex collides with the filamentat a finite time. I will explain the power laws describingthe collision.

Silas AlbenUniversity of Michigan, [email protected]

MS40

Improving Vortex Models for Agile Bio-inspiredFlight via Optimal Control Theory

We formulate a constrained minimization problem whichallows us to relax the usual edge regularity conditions ofpoint vortex models in favor of empirical determination ofvortex strengths. The strengths are determined by mini-mizing the error with respect to empirical force data, whilevortex positions are allowed to evolve freely. We show that,for a flat plate undergoing various maneuvers, the opti-mized model leads to force predictions remarkably close toempirical data.

Jeff D. EldredgeUniversity of California, Los AngelesMechanical & Aerospace [email protected]

Maziar HematiUniversity of California, Los [email protected]

MS40

Dipole Interactions in Doubly-periodic Domains

We consider the interactions of finite dipoles in a doubly-periodic domain as a model that captures the “far-field hy-drodynamic interactions in fish schools. A finite dipole is apair of equal and opposite strength point vortices separatedby a finite distance. We examine the dynamic evolutionsof single dipoles and dipole pairs per box and focus on thestability of two families of relative equilibria: rectangular(1 dipole/box) and diamond (2 dipoles/box). We concludeby commenting on the insights these models offer in thecontext of fish schooling.

Eva Kanso, Alan Cheng Hou TsangUniversity of Southern [email protected], n/a

MS40

Vortex Dipoles

Point vortices of opposite strength propagate at a con-stant speed proportional to the inverse of their separation.Hence a straightforward Matched Asymptotic Expansionapproach struggles to produce the appropriate equationsfor the motion of a vortex dipole, that is a singularityone order higher than a point vortex. We review vor-tex dipoles, including this limiting process, and also studyquasi-analytic solutions for dipoles with viscosity.

Stefan Llewellyn SmithDepartment of MAEUniversity of California, San [email protected]

Raymond NagemBoston [email protected]

MS40

Numerical Study of Viscous Starting Flow PastFlat Plates

Viscous flow past a finite plate of zero thickness movingnormal to itself with velocity U = U0t

p is investigated nu-

160 DS13 Abstracts

merically, using a high order finite difference method. Thesimulations resolve detailed features of the flow, includingthe singular nature of the starting flow, and the depen-dence of various quantities on the Reynolds number andthe parameter p describing the plate motion. The resultsprovide a basis of comparison to evaluate simpler inviscidmodels for flow separation.

Monika NitscheUniversity of New MexicoDepartment of Mathematics and [email protected]

Ling XuGeorgia State [email protected]

MS41

Perturbed Restricted Few-Body Problems andtheir Applications

This talk will present recent advances in the analysis oforbital dynamics in restricted two, three and four bodyproblems perturbed by a conservative force. In particu-lar, we consider the orbital dynamics of a continuous lowthrust spacecraft and the inhomogeneous gravitational fieldof a celestial body. Novel orbits including displaced non-Keplerian and frozen orbits are identified and applicationsto future Earth and asteroid observation missions are pre-sented. The analytical and numerical tools used to studythese different classes of orbits are described.

James Biggs, Marta Ceccaroni, Colin McInnesUniversity of [email protected], [email protected],[email protected]

MS41

Spacecraft Transfer Trajectory Design ExploitingResonant Orbits and Manifolds in Multi-BodyRegimes

The application of dynamical systems techniques to tra-jectory design has demonstrated that leveraging invariantmanifolds and resonant orbits expand the trajectory de-sign options. Transfer trajectories between two- and three-dimensional resonant orbits are explored in a three-bodysystem via Poincar mapping techniques. Incorporatingstrategic maneuvers, trajectories that support various mis-sion scenarios can be constructed.

Kathleen C. HowellPurdue UniversityWest Lafayette, IN [email protected]

Mar VaqueroPurdue Universityn/a

MS41

Dynamics in Astronomical and AstrodynamicalProblems

In this talk it will be shown how modern techniques ofthe Dynamical Systems field are able to provide tools toexplain in a natural way different astronomical patternsas well as to simplify and make more systematic mission

analysis.

Josep MasdemontDepartament de Matematica AplicadaUniversitat Politecnica de [email protected]

Gerard GomezDepartament de Matematica AplicadaUniversitat de [email protected]

MS41

Constant Sun Angle Solar Sail Trajectories

The natural trajectories of spacecraft with solar sails thatare maintained at constant angles to their sun lines aredescribed. The six dimensional equations of motion are re-duced to a two dimensional hodograph equation for themotion in the instantaneous orbital plane. This drivesanother two dimensional equation for the motion of theorbital plane itself. All possible trajectories are classi-fied, and potential applications to trajectory design aredescribed.

Brian StewartUniversity of [email protected]

Phil PalmerSurrey Space [email protected]

Mark RobertsUniversity of Surrey, [email protected]

MS41

Attainable Sets, Fast Numerical Approximation ofInvariant Manifolds and Applications

The paper presents the attainable sets, i.e., admissible low-thrust trajectories and the approximation of invariant man-ifolds with fast numerical methods based on splines. Thesefeatures are used in the preliminary design of transfer tra-jectories defined in a typical three-body problem. Eachfeature provides a trajectory that is based on a reducednumber of parameters, so that transfer trajectories can befound by matching the corresponding parameters of thedifferent trajectory arcs. Examples are provided with ref-erence to transfer between Libration point orbits.

Francesco Topputo, Franco Bernelli-ZazzeraPolitecnico di [email protected], [email protected]

Giorgio MingottiUniversity of [email protected]

Renyong ZhangNorthwestern Polytechnical [email protected]

MS42

Epidemics Dynamics in a City: A Network Model

DS13 Abstracts 161

and Season Variations

We are considering a model for dengue epidemics spread-ing in a densely populated town, where people move dailyfrom one neighborhood to another. For this purpose weconsider a network generalization of SIR model with andwithout birth and death. We are particularly interested inunderstanding how the geometry of the network, its homo-geneity or non homogeneity, the flux of people and a pos-sible seasonal periodicity of climate have an effect in theoccurrence of an epidemics. [Bacaer and Gomez, “On thefinal size of epidemics with seasonality’, Bulletin of Math-ematical Biology, 71 : 1954-1966 (2009); Howard Weiss,“A Mathematical Introduction to Population Dynamics’,IMPA (2009); Lucas Stolerman, Master thesis, “Um Mod-elo em Rede para a dinamica de uma epidemia em umacidade’ (2012); Horst R. Thieme, Mathematics in Popula-tion Biology, Princeton (2003)]

Stefanella BoattoUniversdade Federal de Rio de Janeiro, Brazils [email protected], [email protected]

MS42

Branching Process Models for HIV and SIV Infec-tion

Differential equation models for HIV and SIV infection areof questionable validity when the numbers of a player in themodel (virus or infected cell) are small. We have workedon branching process models for very early infection andsuccessfully treated infection. Although direct simulationis always an option, analytic or mixed methods are oftenpossible. I will summarize our progress and outline direc-tions for future work.

Daniel CoombsUniversity of British [email protected]

Jessica M. ConwayUniversity of British ColumbiaDepartment of [email protected]

Bernhard KonradInstitute of Applied MathematicsUniversity of British [email protected]

Alejandra Herrera ReyesUniversity of British ColumbiaDepartment of [email protected]

MS42

Modeling Dengue Fever: Recent Developments

Dengue is the most significant mosquito-borne viral infec-tion of humans, causing 50-100 million infections annually.The main line of attack against dengue has been traditionalmosquito control measures, such as insecticides. The com-ing years will see the broadening of our anti-dengue arse-nal to include genetically-modified mosquitoes, biocontrolmethods such as Wolbachia, and vaccines. In this talk, Iwill discuss mathematical modeling that is being used tohelp design dengue control efforts using one, or a combina-

tion, of these methods.

Alun LloydNorth Carolina State Universityalun [email protected]

MS42

Sharing Infectious-Disease Risk Across Communi-ties

In recent research, we have combined economic theory andpopulation biology, and explored how the interactions ofbiology and management dynamics can alter the nature ofsocial planning choices, and predicting the emergence ofpolicy-resistance or policy-reinforcement. These theoret-ical advances, however, have relied on strong-mixing as-sumptions. But in many situations, financial, spatial, andsocial heterogeneities which make the problem of policy de-sign much more vexing. In this talk, I’ll present some ofour recent research on the influences of heterogeneity onthe stability of management practices across a spectrum ofscales.

Timothy C. RelugaDepartments of Mathematics and BiologyPennsylvania State [email protected]

MS43

Curvature-Dependent Excitation Propagation inCultured Cardiac Tissue

Excitation front bent above critical value may cease topropagate and give origin to re-entry. We found that in car-diac tissue culture with normal excitation, neither narrowisthmuses nor sharp corners of obstacles affect wave prop-agation. Curvature related propagation block and wavedetachment from obstacles observed only after Lidocainepartial suppression of sodium channels. Computer simu-lations confirmed experimental observations. That is non-inhibited single cells keep excite neighbors irrespective ofcurvature radii smaller than cardiomyocyte size.

Konstantin AgladzeInstitute for Integrated Cell-Material Sciences,Kyoto [email protected]

MS43

Asymptotic Dynamics of Spiral and Scroll Waves ina Mathematical Model of Ischaemic Border Zone

We use asymptotics based on response functions to pre-dict dynamics of re-entrant excitation waves in a movingboundary of a recovering ischaemic cardiac tissue, due togradients of cell excitability and cell-to-cell coupling, andheterogeneity of individual cells. In three spatial dimen-sions, theory predicts conditions for scroll waves to escapeinto the recovered tissue, where they are either collapse ordevelop fibrillation-like state, depending on filament ten-sion. We confirm these predictions by direct simulations.

Irina BiktashevaUniversity of [email protected]

Vadim N. BiktashevCollege of Engineering, Mathematics and PhysicalSciences

162 DS13 Abstracts


Narine SarvazyanGeorge Washington [email protected]

MS43

Dynamics of Spiral Waves on Non-UniformlyCurved Anisotropic Surfaces

Spiral waves in two-dimensional excitable media have beenobserved to drift according to shape of the surface, as wellas due to the anisotropy within the surface. We present aunified mathematical description to these effects using theequivalence of an anisotropic excitable medium to a Rie-mannian manifold. The resulting equation of motion forthe spirals rotation center allows to determine trajectoriesand the position of attractors for spiral waves on the sur-face. The results are applicable to thin layers of electricallyactive cardiac tissue.

Hans Dierckx, Evelien BrisardDepartment of Physics and AstronomyGhent [email protected], [email protected]

Henri VerscheldeGhent [email protected]

Alexander V PanfilovDepartment of Physics and AstronomyGhent University, [email protected]

MS43

Mechanisms of Low Energy Fibrillation Termina-tion in the Cardiac Muscle. Role of Pinned Vor-tices

We found that the mechanism explaining the experiment[1]: Nature 475, 235-239, 2011 is termination of vorticespinned to local heterogeneities in the heart. During electricfield pulses, a pinning center is effectively a stimulatingelectrode situated exactly in the vortex core. A vortex isterminated when an electric field pulse is delivered duringthe ‘critical time interval’.

Valentin Krinsky

Institut Non Lineaire de Nice (INLN) [email protected]


MS44

Anomalous Diffusion in Granular Flow: FractionalKinetics or Intermediate Asymptotics?

Granular materials do not perform Brownian motion, yetdiffusion is observed because flow causes inelastic collisionsbetween particles. Experiments suggest that this processmight be “anomalous” in the sense that the mean squareddisplacement of particles follows a power law in time withexponent less than unity. We show that such a “paradox”

can be resolved using intermediate asymptotics. We derivethe instantaneous scaling exponent of a macroscopic con-centration profile as a function of the initial distribution.Then, by allowing for concentration-dependent diffusivity,we show crossover from an anomalous scaling (consistentwith experiments) to a normal scaling at long times.

Ivan C. ChristovDept. of Mech. & Aerospace Eng., Princeton University,OldenSt., Princeton, NJ 08544-5263, Tel: [email protected]

Howard A StonePrinceton [email protected]

MS44

Molecular Dynamics Based Calculation of the Co-efficient of Restitution in Collision between TwoIdentical Nanoscale Grains

The Coefficient of Restitution (COR) is a useful phe-nomenological concept for describing the interaction ofmacroscopic bodies. However, little is known about thedetailed microscopic processes. We investigate the CORbetween nanoscale particles of various sizes composed offace-centered cubic (fcc) Lennard-Jones (L-J) atoms vianonequilibrium molecular dynamics simulations. We findthat above a critical collision velocity the COR ∼ v−1.03

weakly dependent on the amount or kind of deformation.We find that the critical collision velocity is a function ofthe particle size and approaches a continuum theoreticalvalue for fcc L-J solid in the limit of large sphere radius.

Surajit SenUniversity of [email protected]

Yoichi TakatoSUNY BuffaloPhysics [email protected]

MS44

Visualization of the Dynamics of Granular FlowModels

We will present some recent results from our ongoing re-search on the effective visualization and structural analysisof granular flows. Our work focuses primarily on the studyof both computational simulation and dynamical systemsmodeling of granular systems undergoing tapping bound-ary constraints. We show that an approach leveraging tra-ditional concepts from dynamical systems such as invariantmanifolds and attractors but also graph theoretical con-cepts can reveal interesting properties from such systemsand offer new insights into their behavior.

Xavier M. TricochePurdue UniversityWest Lafayette, IN [email protected]

MS44

Analysis and Simulation of the BSR Model

The BSR model is an integro-partial differential equation

DS13 Abstracts 163

developed to predict granular flows. Using techniques sim-ilar to those employed for the Boltzmann-Enskog equation,we prove that under fairly general assumptions, the BSRmodel has a unique global solution that depends contin-uously on auxiliary conditions. Our proofs inspired thecreation of a semi-discrete numerical scheme for obtainingapproximate solutions of the BSR model, which was usedto produce the results of simulations that will be presented.

Hao WuNew Jersey Institute of TechnologyNewark, NJ 07102 [email protected]

Aminur RahmanNew Jersey Institute of [email protected]

Denis BlackmoreNew Jersey Institute of TechnologyNewark, NJ 07102, [email protected]

MS45

On the Approximation of Transport Phenomena inOcean Dynamics

Over the last years so-called set oriented numerical methodshave been developed for the numerical treatment of dynam-ical systems. We will show how to make use of such tech-niques for the approximation of transport processes. Theseplay an important role in many real world applications, andwe will focus on transport phenomena in ocean dynamics.Here the underlying mathematical models depend explic-itly on time which makes the numerical analysis inherentlymore complicated.

Michael DellnitzUniversity of Paderborn, [email protected]


Chrstian HorenkampUniversity of Paderborn, [email protected]

MS45

Dynamic Programming Using Radial Basis Func-tions

We approximate the optimal value function and the asso-ciated optimal feedback of general nonlinear discrete-timeoptimal control problems by a radial basis function ap-proach. Questions like stability, accuracy and efficiency aswell as code complexity are discussed and demonstrated byselected numerical experiments.

Oliver JungeCenter for MathematicsTechnische Universitaet Muenchen, [email protected]

MS45

Anticorrelated Sampling Techniques for Variance-

reduced Simulation of Markov Processes

Accurate stochastic simulation benefits from reductionof sampling variance and, consequently, computationalcost. We extend classical variance reduction techniques(antithetic and stratified sampling) for application tocontinuous-time Markov jump processes. Our algorithmsintroduce localized anticorrelation between samples to re-duce variance in mean estimates, and apply to both ex-act SSA and approximate tau-leaping simulation methods.Significant reductions in computational cost are achievablefor linear and nonlinear systems, as demonstrated by ana-lytical results and numerical examples.

Peter A. MaginnisMechanical Science and EngineeringUniversity of Illinois at [email protected]

MS45

Weighted Particle Methods for AtmosphericAerosol Simulation

We present a new time-evolution scheme for generating re-alizations of Markov jump processes for particle systems,which can efficiently simulate highly multiscale particledistributions and disparate event rates. Multiscale par-ticle distributions are represented as weighted point sam-ples, and time evolution occurs using a binned tau-leapingscheme with approximate rate sampling. A convergenceproof is given as well as numerical examples of applicationsto atmospheric aerosol particle simulation.

Matthew WestMechanical Science and EngineeringUniversity of Illinois at [email protected]

MS46

Mathematical Modeling of Nanofluids: Propertiesand Applications in the Renewable Energy andBiomediacal Field

Nanofluids are colloids containing a liquid phase, (usuallywater or ethylene), and nanoparticles (usually gold or ox-ides) or nanotubes (usually carbon nanotubes) with diam-eter below 100 nm. Classical models fail to accurately de-scribe their thermal conductivity (depending on nanopar-ticles concentration), and thus their behavior; novel mod-els are being proposed. In this talk we present some re-sults (analytical and numerical), towards applications ofnanofluids in the renewable energy and biomedical field

Federica Di MicheleIIT - Istituto Italiano di TecnologiaScuola Superiore Sant’ Anna, Pisa, [email protected]

Barbara Mazzolai, Edoardo SinibaldiIstituto Italiano di TecnologiaCenter for [email protected]@iit.it, [email protected]

MS46

The Mathematical Modelling and Numerical Sim-ulation of Organic Photovoltaic Devices

We present some recent results and ongoing work on drift-diffusion-reaction systems modelling organic photovoltaic

164 DS13 Abstracts

devices. While classical semiconductors show recombina-tion typically throughout the whole device feature organicphotovoltaic devices significant charge generation only inthe very proximity of an interface between two different or-ganic polymers. We discuss basic questions of modelling,existence and stationary states. Moreover, we present someinteresting asymptotic approximations and discuss the useof entropy.

Klemens FellnerInstitute for Mathematics and Scientific ComputationUniversity of Graz, [email protected]

Daniel BrinkmanDAMTPUniversity of Cambridge, [email protected]

MS46

Solar Updraft Towers for High Latitudes

This presentation is concerned with the modelling and sim-ulation of solar updraft towers with sloped collector fieldsin higher latitudes. The main idea is to study if the re-duction of the solar power (per aerea) at higher latitudescan be compensated by a special non-planar collector ofthe power plant. For this the gas dynamics in the col-lector and in the chimney of the power plant has to bedescribed. I comes out that this is a typical low Machnumber flow and therefore an appropriate low Mach num-ber asymptotics leads to a resonable reduced model. Thislimit model is going to be simulated. Comparisons withplanar power plants and with estimates of the power out-put from the literature are presented.

Ingenuin GasserUniversity of HamburgDepartment of [email protected]

Muhammad Junaid KambohDepartment of MathematicsUniversity of Hamburg, [email protected]

MS46

Renewable Energy Incentive Schemes: Perfor-mance Comparison Using Optimal Control

To meet renewable energy targets, many governments haveinstituted incentive schemes for renewable electricity pro-ducers that aim to boost growth in renewable energy indus-tries. Our work examines four such schemes; we present ageneralised mathematical model of industry growth, and fitthe model with data from the UK onshore wind industry.We consider the optimization of the quantity and timing ofsubsidy through each scheme, and conclude by comparingtheir relative performance.

Neeraj Oak

Bristol Centre for Complexity Science (BCCS)University of bristol, [email protected]

Alan R. ChampneysUniversity of [email protected]

Daniel LawsonDept. of MathematicsUniversity of Bristol, [email protected]

MS47

On the Existence and Stability of Solitary-waveSolutions to a Class of Evolution Equations ofWhitham Type

We consider a class of pseudodifferential evolution equa-tions of the form ut + (n(u) + Lu)x = 0, in which L isa linear smoothing operator and n is at least quadraticnear the origin; this class includes the Whitham equation.Solitary-wave solutions are found using constrained min-imisation and concentration-compactness methods. Thesolitary waves are approximated by the corresponding solu-tions to partial differential equations arising as weakly non-linear approximations; in the case of theWhitham equationthe approximation is the Korteweg-deVries equation. Thefamily of solitary-wave solutions is shown to be condition-ally energetically stable.

Mats EhrnstromDepartment of Mathematical SciencesNorwegian University of Science and [email protected]



MS47

Existence and Conditional Energetic Stability ofSolitary Gravity-capillary Water Waves with Con-stant Vorticity

We present an existence and stability theory for gravity-capillary solitary waves with constant vorticity on the sur-face of a body of water of finite depth. Exploiting aclassical variational principle, we prove the existence of aminimiser of the wave energy E subject to the constraintI = 2μ, where I is the wave momentum and 0 < μ 1.Since E and I are both conserved quantities a standardargument asserts the stability of the set Dμ of minimisers:solutions starting near Dμ remain close to Dμ in a suitablydefined energy space over their interval of existence. Inthe applied mathematics literature solitary water waves ofthe present kind are modelled as solutions of the long-waveequations of KdV or NLS type. We show that the wavesdetected by our variational method converge (after an ap-propriate rescaling) to solutions of the appropriate modelequation as μ ↓ 0.



DS13 Abstracts 165

MS47

On the Benjamin-Feir Instability

I will speak on the Benjamin-Feir (or sideband) instabilityof Stokes waves on deep water. I will begin by describingthe variational framework that I recently developed withBronski to determine an instability under long wavelengthsperturbations for abstract Hamiltonian systems. I will ex-plain the asymptotic approach that Johnson and I adaptedfor Whitham’s water wave model, deriving a dispersion re-lation for the modulational instability. I will discuss on theexact water wave problem, if time permits.

Vera Mikyoung HurUniversity of Illinois at [email protected]

Jared BronskiUniversity of Illinois Urbana-ChampainDepartment of [email protected]

Mathew JohnsonUniversity of [email protected]

MS47

Large-amplitude Solitary Water Waves with Vor-ticity

We provide the first construction of exact solitary waves oflarge amplitude with an arbitrary distribution of vorticity.We use continuation to construct a global connected set ofsymmetric solitary waves of elevation, whose profiles de-crease monotonically on either side of a central crest. Thisgeneralizes the classical result of Amick and Toland.

Miles WheelerDepartment of MathematicsBrown [email protected]

MS48

Shearless Elliptic LCS, Shearless Cantori and non-local heat transport

We present a notion of shearless barriers in unsteady flowsand a method for their accurate detection. This comple-ments recent work on hyperbolic and shear transport bar-riers by G. Haller and F.J. Beron-Vera. We then discusshow shearless Cantori act as partial barriers for heat trans-port in magnetically confined plasma. We investigate theslow relaxation of heat across the Cantori and the strongnon-locality of the relaxation process.

Daniel BlazevskiDepartment of Mechanical and Process EngineeringETH [email protected]

Diego Del-Castillo-NegreteOak Ridge National [email protected]

Mohammad FarazmandPhD student, Mathematics, ETH [email protected]


MS48

Onset of Shearless Tori in Twist Maps

Secondary shearless tori were analytically predicted forgeneric maps in the neighborhood of the tripling bifurca-tion of elliptic fixed points. For the twist standard map,we use numerical profiles of the internal rotation numberto identify the onset of secondary shearless tori around el-liptic fixed points within islands of stability. Moreover, weuse the proposed procedure to find shearless tori in a mapdescribing chaotic magnetic field lines escape in tokamaks.

Ibere L. CaldasInstitute of PhysicsUniversity of Sao [email protected]

Celso AbudUniversity of Sao [email protected]

MS48

Annular Billiard Dynamics in a Circularly Polar-ized Laser Field

We model the dynamics of a valence electron of buckmin-sterfullerene C60 subjected to a circularly polarized laserby the motion of a charged particle in an annular billiard.Its phase space is composed by three distinct types of tra-jectories: whispering gallery orbits which hit only the outerwall; daisy orbits which hit both walls; and ”pringle orbits”that only visit the downfield part of the billiard. This ro-bust separation is attributed to the existence of twistlesstori.

Cristel ChandreCentre de Physique Theorique - [email protected]

Adam KamorGeorgia Institute of [email protected]

Francois MaugerCentre de Physique TheoriqueAix-Marseille [email protected]

Turgay UzerGeorgia Institute of [email protected]

MS48

Breakup of Shearless Tori in Multi-harmonic Area-preserving Nontwist Maps

I will discuss recent work on the breakup of shearless in-variant tori in multi-harmonic nontwist maps, in particu-lar in a two-harmonic, three-parameter map. The breakupthreshold is determined using Greene’s residue criterion.I will report on the effect of map symmetry on torusbreakup, reconnection studies, and the comparison with

166 DS13 Abstracts

a two-harmonic twist map.

Alexander WurmDepartment of Physical & Biological SciencesWestern New England [email protected]

MS49

Conductance Fluctuations in Graphene Systems:The Relevance of Classical Dynamics

Conductance fluctuations associated with transportthrough quantum-dot systems are currently understood todepend on the nature of the corresponding classical dy-namics, i.e., integrable or chaotic. However, we find thatin graphene quantum-dot systems, when a magnetic field ispresent, signatures of classical dynamics can disappear anduniversal scaling behaviours emerge. In particular, as theFermi energy or the magnetic flux is varied, both regular os-cillations and random fluctuations in the conductance canoccur, with alternating transitions between the two. Bycarrying out a detailed analysis of two types of integrable(hexagonal and square) and one type of chaotic (stadium)graphene dot system, we uncover a universal scaling lawamong the critical Fermi energy, the critical magnetic flux,and the dot size. We develop a physical theory based on theemergence of edge states and the evolution of Landau levelsto understand these experimentally testable behaviours.

Celso GrebogiKing’s CollegeUniversity of [email protected]

Lei YingArizona State [email protected]

Liang HuangLanzhou [email protected]

Ying-Cheng LaiArizona State UniversitySchool of Electrical, Computer and Energy [email protected]

MS49

Complex Paths for Regular-to-chaotic TunnelingRates

For generic non-integrable systems we show that a semi-classical prediction of tunneling rates between regular andchaotic phase-space regions is possible. Our prediction isbased on complex paths which can be constructed despitethe obstacle of natural boundaries. The tunneling rates areshown to have excellent agreement to numerical rates forthe standard map where few complex paths dominate. Thisgives a semiclassical foundation of the long-conjectured andoften observed exponential scaling with Planck’s constantof regular-to-chaotic tunneling rates.

Roland KetzmerickInstitut fur Theoretische PhysikTechnische Universitat [email protected]

MS49

Application of Chaos in Harnessing Quantum Sys-tems: Modulating Quantum Transport by Tran-sient Chaos

We propose a scheme to modulate quantum transport innanostructures based on classical chaos. By applying ex-ternal gate voltage to generate a classically forbidden re-gion, transient chaos can be generated and the escape rateassociated with the underlying non-attracting chaotic setcan be varied continuously by adjusting the gate volt-age. We demonstrate that this can effectively modulatethe quantum conductance-fluctuation patterns. A theorybased on self-energies and the spectrum of the generalizednon-Hermitian Hamiltonian of the open quantum system isdeveloped to understand the modulation mechanism. Thisis joint work with Ryan Yang (ASU), Liang Huang (ASU),Louis M. Pecora (NRL), and Celso Grebogi (Univ. Ab-erdeen, UK).

Ying-Cheng LaiArizona State UniversitySchool of Electrical, Computer and Energy [email protected]

MS49

Conductances and Electron Interactions in Regularand Chaotic Quantum Dots

Transmission of electrons through quantum dots leads tointeresting conductance effects in devices. Quantum dotconductance depends on the tunneling barriers to the dotsand the wave functions in the dot. We developed a theoryof conductance through quantum dots including electron-electron interactions. We examined regular and chaotic dotgeometries. The distribution of conductances varies oftenby several orders of magnitude with the dot geometry withchaotic dots having much lower fluctuations than regulardots.

Louis PecoraU.S. Naval Research [email protected]

MS50

The Entropy-Viscosity Method For HydrodynamicModels

The entropy-viscosity technique is a new class of high-ordernumerical methods for approximating scalar conservationlaws which have recently been adapted as a numerical reg-ularization for the Navier-Stokes equations. A nonlinear,LES-type viscosity is based on the numerical entropy resid-ual, causing the numerical dissipation to become large inthe regions of (numerical) shock, and small in the regionswhere the solution remains smooth. This method appliesto systems with one or more entropy inequalities and is easyto implement on a large variety of meshes and polynomialapproximations. I will discuss this method as a numericalregularization for the Navier-Stokes equations, along withrelated regularizations and applications to other equationsif time permits.

Adam LariosDepartment of MathematicsTexas A&M [email protected]

DS13 Abstracts 167

MS50

Spectral Scaling of the NS-α and Leray-α Modelfor Two Dimensional Turbulence

Viewed from the Large Eddy Simulation point of view, theα turbulence models modify the nonlinearity in the NSE,which adaptively filters the high wavenumbers and therebyenhances the stability and regularity without affecting thelow wavenumber behavior. One important aspect to in-vestigate is the spectral scaling transition from the ob-served Kolmogorov (for three-dimensional flows) or Kraich-nan (for two-dimensional flows) power laws in the sub-αscales. The spectral scaling roll-off behavior for wavenum-bers representing scales smaller than the lengthscale α hasimportant implications for the computational performanceof the particular α model and especially in its resolutionrequirements. In this talk I will show how one can establishthe characteristic timescale of an eddy of size less than thefilter width α and hence the scaling of the energy spectrumin the sub-α scales for 2D turbulence.

Evelyn LunasinUniversity of [email protected]

Susan KurienTheoretical Division T-7 Los Alamos NationalLaboratory, [email protected]

Mark A. TaylorSandia National Laboratories, Albuquerque, [email protected]

Edriss TitiUniversity of California [email protected]

MS50

Large-eddy Simulation for Lattice Boltzmann Mod-els

Lattice Boltzmann methods receive a growing intetest inthe field of Computational Fluid Dynamics, for both the-oretical and engineering purposes. The closure of the LBequations for turbulent flow simulations in the LES frame-work will be discussed. A interesting point is that thenonlinearities exhibit an exponential form, instead of theusual quadratic form in Navier-Stokes equations

Pierre SagautInstitut Jean Le Rond d’AlembertUniversite Pierre et Marie Curie-Paris 6, Paris, [email protected]

MS50

Reduced-order Modeling of Complex Flows

In many scientific and engineering applications of com-plex flows such as the flow control and optimization prob-lem, computational efficiency is of paramount importance.Thus, model reduction techniques are frequently used. Toachieve a balance between the low computational cost re-quired by a reduced-order model and the complexity ofthe target turbulent flows, appropriate closure modelingstrategies need to be employed. In this talk, we presentreduced-order modeling strategies synthesizing ideas orig-inating from proper orthogonal decomposition and largeeddy simulation, develop rigorous error estimates and de-

sign efficient algorithms for the new reduced-order models.

Zhu WangInstitute for Mathematics and its ApplicationsUniversity of [email protected]

MS51

Coarse-grained Bifurcation Analysis in AgentBased Bodels: Lifting Using Weights

We discuss lifting and restriction operators in coarse-grained bifurcation analysis for Agent-Based Models. Wewill introduce a new lifting strategy, based on weightedrealisations, which requires the solution of a minimisationproblem at each continuation step, allowing an accurateestimation of Jacobian-vector products and optimal con-vergence of the underlying Newton-GMRES solver. Weapply the new lifting strategy to a model of opinion for-mation, interpreting globally-polarised states in terms of acoarse pitchfork bifurcation.

Daniele AvitabileDepartment of Mathematics, University of SurreyUniversity of [email protected]

Rebecca B. HoyleUniversity of SurreyDepartment of [email protected]

Giovanni SamaeyDepartment of Computer ScienceK.U. [email protected]

MS51

Numerical Methods for Stochastic TravellingWaves


Gabriel J. LordHeriot-Watt [email protected]

MS51

Some New Numerical Methods for Stochastic Desand Pdes

We seek numerical methods for second-order stochasticdifferential equations that accurately reproduce the sta-tionary distribution for all values of damping. A com-plete analysis is possible for linear second-order equations(damped harmonic oscillators with noise), where the statis-tics are Gaussian and can be calculated exactly in thecontinuous-time and discrete-time cases. The ”reverseleapfrog” method has remarkably good properties in thepostion variable. The analysis permits the construction ofnew family of explicit partitioned Runge-Kutta methodswhose accuracy coverges to that of the implicit midpointmethod with increasing number of stages. New methodsare illustrated on double-well SDEs and SPDEs.

Grant LytheDepartment of Applied Maths

168 DS13 Abstracts


MS51

The String Method for the Study of Rare Events

Many problems in applied sciences can be abstractly for-mulated as a system that navigates over a complex energylandscape of high or infinite dimensions. Well known ex-amples include nucleation events during phase transitions,conformational changes of bio-molecules, chemical reac-tions, etc. The system is confined in metastable states forlong times before making transitions from one metastablestate to another. The disparity of time scales makes thestudy of the transition event a very challenging task. Inthis talk, we will discuss the string method for the studyof complex energy landscapes and rare events.

Weiqing RenNational University of Singapore and IHPC, [email protected]

MS52

Instability of Travelling Waves in a SingularChemotaxis Model

The parabolic Keller-Segel model is a strongly coupled sys-tem which describes the directed movement of cells towardsthe gradient of a chemical (chemotaxis). We show exis-tence and nonlinear instability of travelling waves in thecase when the coupling in the highest order terms is sin-gular. To handle the resulting unbounded terms in theequations for a perturbed wave we work in exponentiallyweighted function spaces.

Martin MeyriesKarlsruhe Institute of Technology &University of [email protected]

MS52

Pattern Formation in Unstable Media in BinaryFluids

We discuss about pattern formation and its asymptotic be-haviour of convective patterns in binary fluid flow. Whenthe conductive state is unstable and the size of the do-main is large enough, finitely many spatially localized time-periodic travelling pulses (PTPs), each containing a certainnumber of convection cells, are generated spontaneously inthe conductive state and are finally arranged at nonuni-form intervals while moving in the same direction. Stronginteractions (collision) among PTPs are important in char-acterizing the asymptotic state.

Yasumasa NishiuraRIES, Hokkaido [email protected]

Takeshi Watanabe, Makoto IimaHiroshima [email protected], [email protected]

MS52

Breathers in Singularly Perturbed Reaction-

diffusion Systems

The existence of stationary pulses can be established for ageneral class of two-component, singularly perturbed sys-tems of reaction-diffusion equations. Their (linear) stabil-ity is analyzed using Evans function techniques. For themost general setting, a number of instability results arepresented; detailed analysis of the bifurcation structure isshown in the context of an explicit example. Here, one caneven go beyond the linear analysis; using center manifoldreduction and normal form theory, the nonlinear pulse sta-bility is explored; the latter is inspired by some strikingnumerical results.

Frits VeermanMathematical InstituteLeiden [email protected]

MS52

Stochastic Reaction and Diffusion on Growing Do-mains: Understanding the Breakdown of RobustPattern Formation

Many deterministic mathematical models have been pro-posed to account for the emergence of complexity. How-ever, deterministic systems can often be highly sensitive tochanges in initial conditions, domain geometry, etc. Due tothis sensitivity, we seek to understand the effects of stochas-ticity and growth on paradigm biological patterning mod-els. We do this by using spatial Fourier analysis and grow-ing domain mapping techniques to encompass stochasticTuring systems.

Thomas E. WoolleyOxford University, [email protected]

Ruth BakerUniversity of [email protected]

Eamonn GaffneyMathematical InstituteUniversity of [email protected]

Philip K. MainiCentre for Mathematical BiologyUniversity of [email protected]

MS53

Beyond the Neural Master Equation

We present a stochastic model of neural population dy-namics in the form of a velocity jump Markov process. Thepopulation synaptic variables evolve according to piecewisedeterministic dynamics, which depends on population spik-ing activity. The latter is characterized by a set of discretestochastic variables evolving according to a jump Markovprocess, with transition rates that depend on the synapticvariables. We consider the particular problem of rare tran-sitions between metastable states of a network operating ina bistable regime in the deterministic limit. Assuming thatthe synaptic dynamics is much slower than the transitionsbetween discrete spiking states, we use a WKB approxi-mation and singular perturbation theory to determine themean first passage time to cross the separatrix between

DS13 Abstracts 169

the two metastable states. Such an analysis can also beapplied to other velocity jump Markov processes, such asstochastic ion channel gating and gene networks.

Paul C. BressloffUniversity of Utah and University of Oxford, UKDepartment of [email protected]

MS53

Effective Stochastic Behavior in Dynamical Sys-tems with Incomplete Information

Complex systems are generally analytically intractable anddifficult to simulate. We introduce a method for derivingan effective stochastic equation for a high-dimensional de-terministic dynamical system for which some portion of theconfiguration is not precisely specified. We use a responsefunction path integral to construct an equivalent distribu-tion for the stochastic dynamics from the distribution ofthe incomplete information. We apply this method to theKuramoto model of coupled oscillators to derive an effec-tive stochastic equation for a single oscillator interactingwith a bath of oscillators and also outline the procedurefor other systems.

Carson C. ChowNational Institutes of [email protected]

MS53

The Impact of Architecture on Higher OrderStatistics of Network Dynamics

How does network architecture impact the level of synchro-nized spiking activity in a recurrent network? We showthat for a range of network architectures, average pairwisecorrelation coefficients can be closely approximated usingonly three statistics of network connectivity: the connec-tion probability, and the frequencies of two second ordermotifs. We also discuss how relation between higher orderstatistics of network dynamics and connectivity.

Kresimir JosicUniversity of HoustonDepartment of [email protected]

MS53

Capturing Effective Neuronal Dynamics in Ran-dom Networks with Complex Topologies

We introduce a random network model in which one canprescribe the frequency of second order edge motifs. Wederive effective equations for the activity of spiking neuronmodels coupled via such networks. A key consequence ofthe motif-induced edge correlations is that one cannot de-rive closed equations for the average activity of the nodes(the average firing rate of neurons) but instead must de-velop the equations in terms of the average activity of theedges (the synaptic drives). As a result, the network topol-ogy increases the dimension of the effective dynamics andallows for a larger repertoire of behavior. We demonstratethis behavior through simulations of spiking neuronal net-works.

Duane NykampSchool of MathematicsUniversity of Minnesota

[email protected]

MS54

Termination of Reentrant Cardiac Action PotentialPropagation Using Far-Field Electrical Pacing

Previously, we demonstrated that there exist patterns ofweak electric field stimuli that can terminate fibrillation inthe heart, when fibrillation is modeled as multiple actionpotential waves circulating around one-dimensional rings.In the present work, we extend our fibrillation model to thecase of multiple spiral waves. If this approach is successful,it could lead to new, low-energy defibrillation protocolsthat cause less harm and trauma to patients when applied.

Niels F. OtaniDept. of Biomedical SciencesCornell [email protected]

MS54

Spiral Waves and the Onset of Labor in PregnantUterus

The spontaneous appearance of uterine contractionsshortly before labor is not yet fully understood. Partic-ularly surprising is the fact that none of the uterine cellsis spontaneously oscillating, when taken in isolation. Thestrong increase of the gap junction expression before de-livery strongly suggests a prominent role of the coupling.I will discuss models of excitable cells, coupled to passivecells. In finite tissues, fast spiral waves of electrical activityare spontaneously observed. I will discuss their role, in re-lation with the generation of force necessary for mechanicalcontraction.

Alain PumirLaboratoire de PhysiqueEcole normale superieure de [email protected]

MS54

Anchoring of Spirals

Anchoring of spiral and scroll waves in excitable media hasattracted considerable interest in the context of cardiac ar-rhythmias. Here, by bombarding inclusions with driftingspiral and scroll waves, we explore the forces exerted byinclusions onto an approaching spiral and derive the equa-tions of motion governing spiral dynamics in the vicinity ofinclusion. We demonstrate that these forces nonmonotoni-cally depend on distance and can lead to complex behavior:(a) anchoring to small but circumnavigating larger inclu-sions; (b) chirality-dependent anchoring.

Christian ZemlinFrank Reidy Research Center for BioelectricsOld Dominion [email protected]

Marcel Wellner, Arkady PertsovSUNY Upstate Medical [email protected], [email protected]

MS54

Selection of Spiral Waves in Excitable Media with

170 DS13 Abstracts

a Phase Wave at the Wave Back

A free-boundary approach is elaborated to derive universalrelationships between the medium excitability the param-eters of a rigidly rotating spiral wave in excitable media,where the wave front is a trigger wave and the wave back isa phase wave. Two universal limits restricting the existencedomain of spiral waves in the parameter space are demon-strated. The predictions of the free-boundary approach arein good quantitative agreement with results from numericalreaction-diffusion simulations.

Vladimir ZykovMax Planck Institute for Dynamics and [email protected]

Noriko Oikawa, Eberhard BodenschatzMPI DS [email protected],[email protected]

MS55

Population Scale Physiologic Measurement, Dy-namics, Prediction, and Control

In this talk I will discuss various methodologies for de-riving and explaining data-driven physiologic signals de-rived from clinically collected physiologic data and some ofthe results that these methodologies have generated. Theparticular results will be primarily related to endocrine(e.g., glucose/insulin) and neurophysiologic dynamics. Themethodologies range from signal processing, informationtheory and nonlinear time series analysis to mechanisticphysiologic modeling that hints at potential applicationsof data assimilation and control theory.

David J. AlbersColombia [email protected]

MS55

Capturing Intermittent and Low-frequency Vari-ability in High-dimensional Data through Nonlin-ear Laplacian Spectral Analysis

Nonlinear Laplacian spectral analysis (NLSA) is a methodfor spatiotemporal analysis of high-dimensional data,which represents spatial and temporal patterns throughsingular value decomposition of a family of maps acting onscalar functions on the nonlinear data manifold. Throughthe use of orthogonal basis functions (determined by meansof graph Laplace-Beltrami eigenfunction algorithms) andtime-lagged embedding, NLSA captures intermittency, rareevents, and other nonlinear dynamical features which arenot accessible through classical linear approaches such assingular spectrum analysis. We present applications ofNLSA to detection of decadal and intermittent variabil-ity in the North Pacific sector of comprehensive climatemodels, and multiscale physical modes of the Madden-Julian Oscillation in infrared brightness temperature satel-lite data.

Dimitris GiannakisNew York [email protected]

MS55

Data Assimilation of Biological Dynamics

We have successfully applied a Data Assimilation (UKF)framework centered on the Unscented Kalman Fil-ter (UKF) to track and reconstruct dynamics frombiologically-inspired models of both sleep regulation and ofglucose. Tools weve implemented include a ranked assess-ment of observability, optimization of UKF covariance in-flator, parameter estimation and tracking. The next stepsto apply to read data streams are to address how to differ-entiate between models to best observe real systems.

Bruce J. GluckmanPenn State [email protected]

MS55

Random Dynamics from Time Series: An Overviewin Relation to Noise-induced Phenomena

Interaction between deterministic chaos and stochastic ran-domness has been an important problem in nonlinear dy-namical systems studies. Noise-induced phenomena areunderstood as drastic change of natural invariant densitiesby adding external noise to a deterministic dynamical sys-tems, resulting qualitative transition of observed nonlinearphenomena. Stochastic resonance, noise-induced synchro-nization, and noise-induced chaos are typical examples.The simplest mathematical model for these phenomenais one-dimensional map stochastically perturbed by noise.In this presentation, we discuss typical behavior of noiseddynamical systems based on numerically observed noise-induced phenomena. Applications of these phenomenolo-gies to time-series analysis are also exhibited.

Yuzuru SatoRIES, Hokkaido [email protected]

MS56

New Developments in Evans Function Computa-tion and Shock Layer Stability

We examine some our latest techniques in Evans functioncomputation and apply them to problems in compressiblefluid flow. Specifically, we describe a new way to locateand track roots of the Evans function and apply them toproblems in combustion. We also describe some of ourlatest results in the computation of viscous shock layersin compressible Navier-Stokes and other related models.Finally, we discuss some recent changes to our numericalSTABLAB toolbox.

Jeffrey HumpherysBrigham Young [email protected]

Blake BarkerIndiana [email protected]

Gregory LyngDepartment of MathematicsUniversity of [email protected]

Joshua Lytle

DS13 Abstracts 171

Brigham Young [email protected]

Kevin ZumbrunIndiana [email protected]

MS56

The Morse and Maslov Indices for Matrix Hill’sEquations

For Hill’s equations with matrix valued periodic potential,we discuss relations between the Morse index, countingthe number of unstable eigenvalues, and the Maslov index,counting the number of signed intersections of a path in thespace of Lagrangian planes with a fixed plane. We adaptto the one dimensional periodic setting the strategy of arecent paper by J. Deng and C. Jones relating the Morseand Maslov indices for multidimensional elliptic eigenvalueproblems.

Christopher JonesUniversity of North Carolina and University of [email protected]

Yuri LatushkinDepartment of MathematicsUniversity of [email protected]

Robert MarangellUniversity of [email protected]

MS56

Coherent Structures in a Model for Mussel-algaeInteraction

We consider a model for formation of mussel beds on softsediments. The model consists of coupled nonlinear pdesthat describe the interaction of mussel biomass on the sed-iment with algae in the water layer overlying the musselbed. Both the diffusion and the advection matrices in thesystem are singular. We use Geometric Singular Pertur-bation Theory to capture nonlinear mechanisms of patternand wave formation in this system.

Vahagn ManukianMiami University [email protected]

Anna GhazaryanDepartment of MathematicsMiami University and University of [email protected]

MS56

Linear Stability and Instability of Water Waves

In this talk, I will discuss linear stability and instabilityregions for several water-wave models such as the Benney-Luke equation and the Klein-Gordon periodic waves. Theresults take advantage of the abstract stability criteria de-veloped recently to compute the threshold speed of thestable waves when explicit solutions are known. In caseswhen explicit formulas for the waves are not available, we

compute the stability regions numerically.

Milena StanislavovaUniversity of Kansas, LawrenceDepartment of [email protected]

MS57

Microscale Granular Crystals and Surface AcousticWaves

Granular crystals are densely packed arrays of elastic parti-cles that interact nonlinearly via Hertzian contact. Studieshave demonstrated myriad nonlinear dynamical phenom-ena to occur in granular crystals, and shown how suchphenomena can be utilized in acoustic engineering appli-cations. Thus far, granular crystals are generally macro-scopic, and affect sonic-frequency acoustic waves. In thiswork, we study the interaction of surface acoustic waves(with frequencies in the hundreds of MHz), with two-dimensional microscale granular crystals.

Nicholas BoechlerCalifornia Institute of [email protected]

MS57

On the Existence of Breathers in Periodic Media:An Approach via Inverse Spectral Theory

The concept of breathers, i.e. time-periodic, spatially lo-calized excitations, has been introduced in the context ofthe Sine-Gordon equation, which, however, seems to be theonly (constant coefficient) nonlinear wave equation to sup-port such solutions. In this sense, breathers have been con-sidered a rare phenomenon. Surprisingly, a nonlinear waveequation with spatially periodic step potentials has beenfound recently to support breathers (Blank et al. 2011)by using a combination of spatial dynamics, center mani-fold reduction and bifurcation theory. Via inverse spectraltheory, we aim towards characterizing a larger class of po-tentials that allow breathers. The research is motivated bythe quest of using photonic crystals as optical storage.

Martina Chirilus-Bruckner, C.E. WayneBoston [email protected], [email protected]

MS57

Multi-dimensional Stability of Travelling Wavesthrough Rectangular Lattices

We consider general reaction diffusion systems posed onrectangular lattices in two or more spatial dimensions.We show that travelling wave solutions to such systemsthat propagate in rational directions are nonlinearly sta-ble under small perturbations. We employ recently devel-oped techniques involving point-wise Green’s functions es-timates for functional differential equations of mixed type(MFDEs), allowing our results to be applied even in situ-ations where comparison principles are not available.

Hermen Jan HupkesUniversity of LeidenMathematical [email protected]

Aaron HoffmanFranklin W. Olin College of Engineering

172 DS13 Abstracts

[email protected]

Erik Van VleckDepartment of MathematicsUniversity of [email protected]

MS57

Macroscopic Analysis of Traveling Waves in Micro-scopic Traffic Models

The traffic jam dynamics of a microscopic model is ana-lyzed on a macroscopic level, i.e., for characteristic low-dimensional quantities, using an implicit equation-free ap-proach. These methods are used to analyze the qualita-tive system behaviour by coarse bifurcation diagrams. Thetransitions from free flow to different traffic jam regimes,i.e., traveling waves on the ring road, are investigated, in-cluding one pulse and two pulse solutions.

Christian MarschlerDanmarks Tekniske UniversitetInstitut for [email protected]

Jan SieberUniversity of [email protected]

Jens StarkeTechnical University of DenmarkDepartment of [email protected]

MS58

Melnikov Theory for Planar Hybrid Systems: In-variant Cones in Piecewise Linear Systems

We extend the Melnikov theory to a class of two-zonal pla-nar hybrid piecewise smooth systems. In these systems,each zone of differentiability is separated by a straight line.When an orbit reaches the separation line then a reset mapapplies before entering the orbit in the other zone. By usingMelnikov functions we analyze the existence of limit cycles.The results will be applied to the study of invariant conesin 3D piecewise linear systems.

Victoriano CarmonaDepartamento de Matematica Aplicada IIUniversidad de Sevilla, [email protected]

Soledad Fernandez-GarciaDepartamento Matematica Aplicada IIUniversity of Seville, [email protected]

Emilio Freire, Francisco TorresDepartamento Matematica Aplicada IIUniversidad de Sevilla, [email protected], [email protected]

MS58

On the Splitting of Heteroclinic Manifolds in Cou-pled Systems with Impacts

In this work we consider two coupled impact systems ob-

tained by a generalization of the model of the rocking block.After introducing a general perturbation, which includesboth the coupling and an external periodic forcing, we ex-tend Melnikov’s method to this type of system to provideconditions for the persistence of heteroclinic manifolds. Wealso study properties regarding the energy accumulatedalong trajectories located in these manifolds.

Albert GranadosIPVS, University of Stuttgartalberto.granados [email protected]

Tere M. SearaUniv. Politecnica de [email protected]


MS58

Application of the Subharmonic Melnikov Methodto Piecewise Smooth Systems

We extend a refined version of the subharmonic Melnikovmethod to piecewise-smooth systems and demonstrate thetheory for bi- and trilinear oscillators. Fundamental re-sults for approximating solutions of piecewise-smooth sys-tems by those of smooth systems are given and used toobtain the main result. Special attention is paid to degen-erate resonance behavior, and analytical results are illus-trated by numerical ones. Further results on perturbationapproaches for piecewise-smooth systems will also be an-nounced.

Kazuyuki YagasakiDepartment of MathematicsHiroshima University, [email protected]

MS59

Memory Effects of Inertial Particles in Chaotic Ad-vection

We study the effect of the history force in the von Karmanflow, a paradigmatic model flow of chaotic advection. Wefind strong qualitative changes in the dynamics induced bythe history force. Attractors are typically suppressed andmore generally we find a weaker tendency for accumulationand for caustics formation. Furthermore the Lyapunov ex-ponent increases with the history force and the escape ratesare strongly altered.

Anton DaitcheUniversity of [email protected]

Tamas TelEotvos Lorand University, HungaryInst for Theoretical [email protected]

MS59

The Influence of the History Force on the Motionof Inertial Particles in Chaotic Advection: Gravi-

DS13 Abstracts 173

tational Effects and Horizontal Diffusion

In this work we analyze the effect of the Basset force onthe sedimentation of inertial particles in a two-dimensionalconvection flow. When the memory effects are neglected,the system’s dynamics exhibits periodic, quasi-periodic andchaotic attractors. With the history force we find thatthe attractors and their basins of attraction are drasticallyaltered. We also highlight the strong influence of memoryon the horizontal transport and vertical trapping of theparticles.

Ksenia GusevaUniversity of OldenburgOldenburg, [email protected]


MS59

Memory Effects in Chaotic Advection and Snap-shot Attractors

The presence of the history force in the Maxey-Riley equa-tions makes the equation of motion to be an integro-differential equation. Viewed from the usual phase space ofinertial particles, the dynamics is non-autonomous. Aftera short overview of recent results, we concentrate on theproblem of how, say, periodic attractors can emerge in suchsystems. In the general theory of driven, time-dependentdissipative systems, an emerging tool is that of the so-calledsnapshot (or pullback) attractors. Such an attractor is theinstantaneous location, in the phase space, of the elementsof an ensemble of trajectories initiated in the remote past.To any single snapshot attractor there belongs a uniquenatural distribution that typically changes with time. Thisconcept has been proven to be useful in climate models. Weclaim it to be also applicable to the problem of particle ad-vection with history force. In the traditional single particlepicture, a periodic attractor is reached after a power-lawdecay, while the convergence to the (still slowly moving)snapshot attractor is exponentially fast.


MS60

Randomized Algorithms for Very Large-Scale Lin-ear Algebra

Low-rank matrix approximations, such as partial spectraldecompositions, play a central role in data analysis and sci-entific computing. The talk will describe a set of recentlydeveloped randomized algorithms for computing such ap-proximations. These techniques exploit modern computa-tional architectures more fully than classical methods andopen the possibility of dealing with truly massive matri-ces. The algorithms described are supported by a rigorousmathematical analysis that exploits recent work in randommatrix theory.

Gunnar MartinssonUniv. of Colorado at [email protected]

MS60

The Dynamic Mode Decomposition: Extensionsand Variations

Dynamic mode decomposition (DMD) represents an effec-tive means for capturing the essential features of numeri-cally or experimentally generated flow fields. We will dis-cuss various extensions of and variations on the standardalgorithms to promote sparsity by combining tools andideas from linear algebra, convex optimization and com-pressive sensing. Several examples of flow fields resultingfrom simulations and experiments are used to illustrate theeffctiveness of the developed method.

Peter Schmid

Ecole Polytechnique Paris, FranceLaboratoire d’Hydrodynamique (LadHyX)[email protected]

Mihailo R. JovanovicElectrical and Computer EngineeringUniversity of [email protected]

MS60

Data-driven Modeling Approach for Olfaction Dy-namics

In this talk I will introduce a data-driven approach forthe combination of dynamical systems and data-reductionfor neural networks. The approach is particularly relevantto neurobiological networks that underlie sensory systems,e.g., olfaction, for which neural activity is recorded whileactual sensory modality is being processed. Specifically,we will show how to construct the network wiring, i.e.,connectivity and dynamics, from the data via a reducedmodel.

Eli ShlizermanUniversity of Washington, [email protected]

MS60

Dynamic Mode Decomposition with Sub-Nyquist-Rate Data Samples

Dynamic mode decomposition (DMD) is an increasinglypopular tool for identifying oscillatory structures in fluidflows. However, it requires time-resolved data, which areoften impossible to capture experimentally. We presenta new algorithm that can identify temporally oscillatorystructures from sub-Nyquist rate data. This is accom-plished using compressed sensing, taking advantage of thesparsity observed in many flows. As a proof of concept, weapply our method to experimental data from a bluff bodywake.

Jonathan TuPrinceton [email protected]

MS61

Energy Exchanges in Embedded Granular Media

We discuss experimentally energy exchange phenomenain coupled granular chains embedded in poly-di-methyl-siloxane (PDMS) matrix. Specifically, we consider tworows of chains embedded in PDMS matrix and show that

174 DS13 Abstracts

in spite of the fact that applied impulse is provided toone chain, the resulting pulse gets partially transferred toneighboring chain and energy distributes among the granu-lar network. Based on the experimental measurements wevalidate a theoretical model and then use it for predictivedesign.

M. Arif Hasan, Shinhu Cho, Waltraud Kriven, AlexanderVakakisUniversity of [email protected], [email protected],[email protected], [email protected]

MS61

Long Lived Solitary Waves in a 1D Granular Chain

Kinetic energy fluctuations of a non-dissipative 1D gran-ular chain held between reflecting walls with various pre-compressions are investigated. The dynamics is exploredfor a weakly precompressed chain which admits only soli-tary waves that break into secondary waves under wall col-lisions, for a strongly precompressed chain which exhibitsacoustic waves, and for intermediate precompression. Thelast case accommodates a nearly stable solitary wave thattravels unaffected through the acoustic waves for extremelylong times.

Surajit SenUniversity of [email protected]

Yoichi TakatoSUNY BuffaloPhysics [email protected]

MS61

Nonlinear Wave Propagation in the Arrays of Cou-pled Granular Chains

Dynamics of granular scalar models comprising the arrayof the arbitrary number of weakly coupled granular chainssubject to on-site perturbations is considered. Analyticalprocedure depicting the transmission of strongly nonlinear,localized pulses through the granular array is developed.Results of analytical model and numerical simulations arefound to be in a spectacular correspondence. Effect of on-site perturbations on the primary pulse transmission andredirection in the general scalar model is discussed.

Yuli StarosvetskyTechnion, Israel Institute of [email protected]

MS61

Existence of Bell-shaped Traveling Waves inMonomer Chains with Precompression

In a series of joint works with P. Kevrekidis, we showthe existence and bell-shapedness of traveling waves formonomer chains. The novelty is the bell-shapedness of thewaves, which is achieved by recasting as an equivalent con-strained maximization problem, where we constraint overthe unit spheres of certain Orlicz spaces. We will also men-tion some open problems (and possible approaches) likeuniqueness and stability of these waves.

Atanas StefanovUniversity of Kansas

[email protected]

MS62

Modeling Early Events in HIV Infection

In order to prevent and/or control infections it is necessaryto understand their early-time dynamics. However this isprecisely the phase of HIV about which the least is known.To investigate the initial stages of HIV within-host we havedeveloped multi-type, continuous-time branching processmodels. We will present these models and discuss predic-tions pertinent to clinical factors associated with HIV suchas per-exposure risk of infection and post-exposure time toinfection detection.

Jessica M. ConwayUniversity of British ColumbiaDepartment of [email protected]

MS62

SIV Infection Dynamics in Macaques After Inter-ruption of Intensified Treatment

HIV infection is well controlled by anti-retroviral drug ther-apy (ART) but virus persists and viremia returns upontreatment cessation. Recent studies on SIV infected mon-keys showed a complete suppression of viral load duringintensified ART. After treatment stopped, occasional vi-ral blips occur but the viral load always returns to unde-tectable levels. We used models based on continuous-timebranching processes to study the viral blips and make infer-ences about the re-activation dynamics of latently infectedcells.

Alejandra Herrera Reyes, Jessica M. ConwayUniversity of British ColumbiaDepartment of [email protected], [email protected]

Daniel CoombsUniversity of British [email protected]

MS62

A Branching Process Model of Prion Dynamics

Prions are infectious agents composed of misfolded pro-teins, responsible for illnesses such as mad cow disease incattle and Creutzfeldt-Jakob disease in humans. We createa branching process model for yeast cells to describe howprions grow inside the cell and how they are transmittedfrom mother to daughter cell. We compare our model pre-dictions to laboratory data and use it to estimate unknownparameters.

Peter OlofssonTrinity UniversityDepartment of [email protected]

MS62

Brisk Introduction to Branching Processes with aModel of Gene Expression

I will provide a very brief overview of what branching pro-cesses are and what they are useful for modelling. I willthen discuss one novel application to the phenomenon of

DS13 Abstracts 175

gene expression with diffusion in the cellular environment.The latter is joint work with David Cottrell and PeterSwain.

Paul TupperDepartment of MathematicsSimon Fraser [email protected]

MS63

Fatigue Accumulation Under Chaotic Loading isSlower than Under Statistically and SpectrallySimilar Stochastic Excitation

New fatigue testing apparatus was used to show differ-ent rates of fatigue damage accumulation under chaoticand stochastic loading, even when both excitations possesssame spectral and statistical signatures. Furthermore, theconventional rainfall method considerably overestimatesdamage in case of chaotic forcing. Important nonlinearloading characteristics, which can explain the observed dis-crepancies, are identified and suggested to be included asloading parameters in new fatigue models.

David Chelidze, Son Hai Nguyen, Mike Falco, Ming LiuUniversity of Rhode IslandDepartment of Mechanical, Industrial & [email protected], , –, –

MS63

Localized Spikes and Flats on the Surface of Mag-netic Liquids

An experimental model for formation of spatially localizedstates in dissipative systems is a layer of viscous magneticliquid subjected to a magnetic field oriented normally tothe fluid surface. When the field passes a critical threshold,a hexagonal pattern of liquid spikes emerges. Localizedspikes and flats were generated and studied experimentallyand numerically. In contrast to spikes, the location of flatsis arrested by the hexagonal pattern.

Reinhard RichterUniversity of [email protected]

M SzechUniversity of BayreuthDepartment of Physics–

Ingo RehbergExperimentalphysik V, Universitaet Bayreuth95440 Bayreuth, [email protected]

MS63

Bifurcation Analysis in a Mechanical Impact Oscil-lator Experiment

We use control-based continuation to obtain one-parameterbifurcation diagrams (e.g. frequency response) directlyfrom an experiment of a periodically forced impact oscil-lator. Branches of periodic solutions, including unstableones, are traced by applying a feedback control and usinga predictor-corrector type path-following algorithm. Theexperimental findings are reproduced by a piecewise-linear

model. It is smoothed to determine its bifurcation struc-ture and the effect of the smoothening is investigated.

Jens StarkeTechnical University of DenmarkDepartment of [email protected]

Emil BureauTechnical University of [email protected]

Frank Schilder, Michael ElmegaardTechnical University of DenmarkDepartment of [email protected], [email protected]

Jon Juel Thomsen, Ilmar SantosTechnical University of DenmarkDepartment of Mechanical [email protected], [email protected]

Hinke M. Osinga, Bernd KrauskopfUniversity of AucklandDepartment of [email protected], [email protected]

MS63

Control of Nonlinear Lateral Dynamics in a Rotor-Stator System

In this combined experimental and numerical effort, a rotorcontained within a stator is studied. An excitation inputwith high frequency content is superimposed on the motorrotation input provided to the rotor-stator system to ex-amine how the lateral motions of the rotor can be steeredamong different solutions of the system, which include for-ward whirling solutions without rotor contact and forwardand backward whirling solutions with contact.

Nicholas Vlajic, Balakumar BalachandranDept. of Mechanical EngineeringUniversity of [email protected], [email protected]

MS64

Collective Effects and Cascading Dynamics for Sys-tems Defined on Complex Networks

Dynamical systems defined on networks have applicationsin many scientific fields. In particular, it is important tounderstand when networks exhibit synchronous or othertypes of coherent collective behaviors. Other questions in-clude whether such coherent behavior is stable with respectto random perturbation, or what the detailed structureof this behavior is as it evolves. We will examine severalprototypical models of networked dynamical systems andpresent a mixture of results that range from rigorous the-orems for abstract models to quantitative comparisons ofmodels and data.

Lee DeVilleUniversity of Illinois, Department of [email protected]

MS64

Reliable and Unreliable Behavior in Balanced Spik-

176 DS13 Abstracts

ing Networks

This talk concerns the reliability of networks of excitableneurons driven by sustained, fluctuating stimuli. Relia-bility here means that a signal elicits essentially identicalresponses upon repeated presentations, regardless of thenetwork’s initial condition; it is of interest in computa-tional neuroscience because the degree to which a networkis reliable constrains its ability to encode information intemporal spike patterns. Using a combination of qualita-tive theoretical ideas and numerical simulations, we havestudied the dynamics of networks of excitable neurons withbalanced excitatory and inhibitory connections. I will re-port our main findings, including the coexistence of unreli-able and reliable dynamics in time and within the network,and (time permitting) how the correlation structure of thestimulus and intrinsic network dynamics together affect thereliability of a network. Qualitative explanations are pro-posed for the phenomena observed.

Kevin K. LinDepartment of MathematicsUniversity of [email protected]

Guillaume Lajoie, Eric Shea-BrownDepartment of Applied MathematicsUniversity of [email protected], [email protected]

MS64

Spike-based Coding in Chaotic Neural Networks

Large, randomly coupled networks of excitatory and in-hibitory neurons are ubiquitous in neuroscience, and areknown to autonomously produce chaotic dynamics. Thisproduces an obvious threat to the reliability of networkresponses: if the same signal is presented many timeswith different initial conditions, there is no guarantee thatthe system will entrain to the signal in a repeatable way.However, we find that intermittent periods of highly reli-able spiking nevertheless occur in the networks at hand.We give a geometrical explanation, and discuss the conse-quences for encoding and decoding of model sensory sig-nals.


MS64

Maximized Reliability Despite Maximized Vari-ability in Sensory Cortex

An identical sensory stimulus presented many times doesnot typically evoke identical responses among neurons insensory cortex. It is commonly thought that such vari-ability of response is detrimental to reliable encoding ofsensory information. Studying rat cortex slice cultures,we demonstrate that variability need not come at the costof reliability. Pharmacologically tuning excitability of thecortical network we found that maximum reliability andvariability emerge together under the same conditions atcriticality.

Woodrow ShewUniversity of [email protected]

MS65

Defibrillation Mechanisms on a One-dimensionalRing of Cardiac Tissue

In this paper we compare quantitatively the efficiency ofthree different defibrillation protocols commonly used incommercial defibrillators. We have built a simplified one-dimensional model of cardiac tissue using the bidomainformulation that is the standard model for describing car-diac tissue. With this model, we have shown that biphasicdefibrillators are significantly more efficient (about 25 per-cents) than the corresponding monophasic defibrillators.We identify that the increase in efficiency of the biphasicdefibrillators is rooted in the higher proportion of excitedtissue at high electric fields.

Jean BragardDepto de Fisica y Matematica AplicadaUniversidad de Navarra, Pamplona, [email protected]

MS65

Mechanisms of Ventricular Arrhythmias

Complex behavior in the heart often is associated with elec-trical abnormalities called arrhythmias that lead to com-promised mechanical function. Such complexity includesdynamics typical of excitable and oscillatory systems, in-cluding period-2 (and higher-order) behavior along withsingle and multiple spiral or scroll waves. In many cases,dynamical instabilities either produce or exacerbate ar-rhythmias. In this talk, we use mathematical modelingand numerical simulation to elucidate mechanisms that caninitiate and maintain cardiac arrhythmias.


MS65

Cardiac Arrhythmia Prediction Using a 1D Dy-namical Model

A nonlinear mathematical model of a cardiac fiber has beendeveloped to gain improved understanding of the role ofpremature beats in the formation of ventricular fibrillation(VF), a lethal cardiac arrhythmia. The model predictionshave been compared with in vitro data from canine rightventricles, confirming that the model is able to determinewhich sequences of premature beats are more likely to pro-duce VF.

Laura MunozDepartment of Biomedical SciencesCornell [email protected]

Niels F. OtaniDept. of Biomedical SciencesCornell [email protected]

Anna GelzerDepartment of Biomedical SciencesCornell [email protected]

Flavio Fenton

DS13 Abstracts 177

Georgia Institute of [email protected]

Weiye Lin, Min Chul Shin, Andrea LiuDepartment of Biomedical SciencesCornell [email protected], [email protected], [email protected]

Robert Gilmour, Jr.University of Prince Edward [email protected]

MS65

Spiral Wave Generation and Instabilities in Car-diac Systems with Pacemaker-obstacle Interactions

We performed experiments on annular domains of cardiacmonolayers with embedded pacemakers composed of ven-tricular cells from 8-day-old embryonic chick hearts. Wetracked the wave propagation using an intracellular calciumdye and a CCD camera. The monolayers with wider annu-lar domains generated more complex behaviour, includingreentrant wave dynamics. Numerical simulations using asimplified FitzHugh-Nagumo model coupled in space pro-vided insight into the dynamics.

Thomas D. QuailMcGill [email protected]

MS66

Mathematical Models of Crime and Energy Use inUrban Societies


Luis BettencourtSanta Fe [email protected]

MS66

Rate Effects on the Growth of Centres

Much of the mathematical modelling of urban systemsrevolves around the use spatial interaction models, de-rived from information theory and entropy-maximisationtechniques and embedded in dynamic difference equations.This class of models have wide reaching applications: fromtrade and migration flows to the spread of riots and under-standing the spatio-temporal patterns of burglaries. Whenframed in the context of a retail system, the dynamics ofcentre growth poses an interesting mathematical problem,with bifurications and phase changes, which may be anal-ysed analytically. In this contribution, we present someanalysis of the continuous retail model and correspond-ing discrete version, which yields insights into the effect ofspace on the system, and an understanding of why certainretail centers are more successful than others.

Hannah FryCentre for Advanced Spatial Analysis.University College [email protected]

Frank SmithDepartment of Mathematics, University College [email protected]

MS66

What can Dynamical Systems Tell Us About UrbanEnergy Systems?

Cities account for over two-thirds of the world’s primaryenergy consumption and 71% of global energy-relatedgreenhouse gas emissions. To understand and improve theperformance of urban energy systems, a range of modellingtechniques have been used but dynamical systems methodsare not widely employed. This paper will consider why thismight be the case and suggest specific applications wheredynamical systems offer the greatest potential.

James KeirsteadDepartment of Civil and Environmental EngineeringImperial College [email protected]

MS66

Mathematics of Crime

This lecture uses crime as a case study for using appliedmathematical techniques in a social science application andcovers a variety of mathematical methods that are appli-cable to such problems. We will review recent work onagent based models, methods in linear and nonlinear par-tial differential equations, variational methods for inverseproblems and statistical point process models. From an ap-plication standpoint we will look at problems in residentialburglaries and gang crimes. Examples will consider both”bottom up’ and ”top down’ approaches to understandingthe mathematics of crime, and how the two approachescould converge to a unifying theory. We will cover specificexamples where urban geography plays an important rolein the models.

Martin [email protected]

Andrea L. BertozziUCLA Department of [email protected]

MS67

Periodic Waves in Fire-diffuse-fire Model of Cal-cium Dynamics in Cardiac Cells

Calcium dynamics plays an important role in intracellularcommunication in living cells. The fire-diffuse-fire model,which accounts for the effects of diffusion, absorption, andlocalized release of calcium, has been successfully used tomodel the initiation, propagation and failure of calciumwaves and other spatio-temporal patterning of intracel-lular calcium. Previous theoretical studies were usuallyperformed under the assumption of a linear absorptionmechanism. In this talk I will present a simple approachfor studying periodic traveling waves in one-dimensionalfire-diffuse-fire models with an arbitrary absorption mech-anism. I will then describe dynamics of such waves anddiscuss their stability and robustness.

Peter GordonNew Jersey Institute of [email protected]

Louis TaoPeking [email protected]

178 DS13 Abstracts

MS67

A Simple Criterion of Transverse Linear Instabilityfor Nonlinear Waves

Transverse stability refers to the stability of a nonlinearwave which is homogeneous in one spatial direction withrespect to non-homogeneous perturbations. Relying upona spatial dynamics formulation in which the time-like vari-able is the spatial direction in which the wave is homoge-neous, we give a sufficient condition for transverse linearinstability. We apply this criterion to solitary and periodicgravity-capillary water waves.

Mariana HaragusLaboratoire de Mathematiques de BesanconUniversite de Franche-Comte, [email protected]

MS67

Nonlinear Schrodinger Models and PT-Symmetry:Living at the Interface between Hamiltonian andDissipative

This talk concerns a theoretical analysis of some aspectsof a theme that has received particular attention recently,namely parity-time (PT) symmetric media. Such me-dia have recently been realized in nonlinear optics, wherethey often feature a cubic nonlinearity. In this talk, wewill see how this special PT-symmetric interface betweenthe underlying Hamiltonian problem and the presence ofthe gain/loss leads to interesting modifications of the sys-tem’s bifurcations, to the emergence of new, so-called ghoststates and to rather unexpected dynamical implications inboth one and two dimensions.

Panayotis KevrekidisDepartment of Mathematics and StatisticsUniversity of [email protected]

MS67

Stability of Traveling Waves on Vortex Filaments

We develop a general framework for studying the stabilityof solutions of the Vortex Filament Equation (VFE), basedon the correspondence between the VFE and the nonlin-ear Schrodinger (NLS) equation provided by the Hasimotomap. This method is used to investigate the (linear and or-bital) stability of periodic and soliton solutions. In the pe-riodic case, we show that the solutions associated to cnoidalwave solutions of the NLS are stable only in the case wherethey take the form of an unknotted torus knot.

Stephane Lafortune, Annalisa M. CaliniCollege of CharlestonDepartment of [email protected], [email protected]

MS68

Of Slugs and Snakes: Moving Localized Structuresin Fluid Flows

In this talk I will describe the origin and properties of mov-ing spatially localized convection found in different doublydiffusive systems. Two systems will be described in detail:binary fluid convection in a horizontal layer and naturaldoubly-diffusive convection in a vertically extended cav-ity. Although the motion of these structures is generallysluggish their collisions may lead to new types of dynami-

cal behavior. The numerical results will be related to thephenomenon of homoclinic snaking in spatially reversiblesystems. The talk will be based on ongoing work with A.Alonso, O. Batiste, C. Beaume, A. Bergeon and I. Mer-cader.


MS68

Unstable Solitons in Inhomogeneous NonlinearSchrodinger Equations

I will discuss the (in)stability of solitons arising in mod-els used to create a Bose-Einstein Condensate. I will out-line how the Maslov index can be used to establish theinstability of standing waves to inhomogeneous NLS equa-tions. Instability will be established by simple observationsof the initial soliton’s orbit in the phase plane. This tech-nique can be used to show instabilities in excited states,asymmetric states, gap solitons, and solitons on an nonzerobackground.

Robert MarangellThe University of [email protected]

Russell JacksonUS Naval [email protected]

Christopher JonesUniversity of North Carolina and University of [email protected]

Hadi SusantoThe University of NottinghamUnited [email protected]

MS68

Nonlocal Interactions and Localized Patterns

Localized patterns may occur in bistable systems, or frominteractions with large-scale modes, or due to nonlocal in-teractions. This work explores the third of these mecha-nisms, which has received relatively little attention. Nonlo-cal equations with an integral convolution term arise natu-rally in many applications, including neural field modelingand predator-prey systems. We derive amplitude equationsfor such systems that can themselves be pattern-forming,leading to a ”patterns on patterns” structure or stronglylocalized states.

Paul C. Matthews, Madallah AlenaziUniversity of [email protected],[email protected]

Stephen M. CoxUniversity of NottinghamSchool of Mathematical [email protected]

MS68

Oscillons Near Hopf Bifurcations of Planar Reac-

DS13 Abstracts 179

tion Diffusion Equations

Oscillons are planar, spatially localized, temporally oscil-lating, radially symmetric structures. They have been ob-served in various experimental contexts, including fluid sys-tems, granular systems, and chemical systems. Oscillonsoften arise near forced Hopf bifurcations, which are mod-eled mathematically with the forced complex Ginzburg-Landau (FCGL) equation. We present a proof of the exis-tence of oscillons in the forced planar complex Ginzburg-Landau equation through a geometric blow-up analysis.Our analysis is complemented by a numerical continuationstudy of oscillons in the forced Ginzburg-Landau equationusing Matlab and AUTO.

Kelly Mcquighan, Bjorn SandstedeBrown Universitykelly [email protected], bjorn [email protected]

MS69

Fluctuations and Equipartition in the Dynamics ofGranular Ratchets

We examine the motion of a macroscopic wedge-shapedparticle (constrained to only move along the x-axis) en-countering dissipative collisions with granular gas particles.Based on a general stochastic model, we derive the fullPDF of the wedge’s motion. Contrary to what is observedfor a Maxwell-Boltzmann gas, vanishingly small perturba-tions to the gas velocity PDF (e.g. via shaking) result ina steady-state drift velocity independent of wedge mass inthe limit of a massive particle.

Johannes P. Blaschke, Jurgen VollmerMax Planck Institute for Dynamics and [email protected], [email protected]

MS69

Symmetry Breaking Induced Rotating Spirals inAgitated Wet Granular Matter

Pattern formation of a thin layer of vertically agitated wetgranular matter is investigated experimentally. Due to thestrong cohesion arising from the capillary bridges formedbetween adjacent particles, agitated wet granular matterexhibits a different scenario as its dry counter-part. Ro-tating spirals with three arms, which correspond to thekinks between regions with different colliding phases, arethe dominating pattern. This preferred number of arms arefound to be related to the period tripling of the agitatedgranular layer, which breaks the spatiotemporal symme-try and drives the rotation. As symmetry is retained in anarrow regime of the control parameter, period doublingpattern with frozen wave fronts arise. The phase diagramof patterns with breaking and non-breaking symmetries,as well as the shape and rotating speed of spirals will beaddressed.

Lorenz Butzhammer, Ingo RehbergExperimentalphysik V, Universitaet Bayreuth95440 Bayreuth, [email protected], [email protected]

Kai HuangUniversitat [email protected]

MS69

Momentum Transfer in Non-equilibrium SteadyStates

An anisotropic and inelastic Brownian object can showsteady nonequilibrium motion in an equilibrium ideal gas.Despite many adhoc calculations, the essential mechanismof this motion was only recently understood using theconcept of momentum transfer deficit due to dissipation[Fruleux et al. Phys Rev Let.(2012)]. By this concept,many hetherto unrelated phenomena, like adiabatic pistonor Brownian ratchet are also shown to be variants of a classof nonequilibrium steady states.

Ken [email protected]

Antoine FruleuxGulliver, ESPCI, [email protected]

Ryoichi KawaiDepartment of PhysicsUniversity of Alabama at [email protected]

MS69

A Granular Ratchet: Spontaneous SymmetryBreaking and Fluctuation Theorems in a GranularGas

Weexperimentally construct a ratchet of the Smoluchowski-Feynman type, consisting of four vanes that rotate freelyin a vibrofluidized granular gas. We show that a steadystate fluctuation relation holds for the work injected to thesystem, and that its entropy production satisfies a detailedfluctuation theorem. Surprisingly, the above relations aresatisfied even when a convection roll has developed with astrong coupling between the motion of the vanes and thegranular gas.

Devaraj van der MeerUniversity of [email protected]

MS70

Exact Solution to Estimation Problems in ScalarConservation Laws and Hamilton-Jacobi PDEs.Applications to Transportation Engineering

In this talk, we investigate scalar conservation laws (orequivalently Hamilton Jacobi equation) with concave flux,in which initial, boundary and internal conditions are un-certain. Using the properties of the Lax-Hopf solution,we write the problem of reconstructing the intitial, bound-ary and internal conditions as mixed integer convex pro-gramming. The resulting framework is very flexible, andcan compute solutions to various problems associated withtransportation engineering: estimation, boundary control,privacy analysis, cybersecurity.

Christian ClaudelKing Abdullah University of Science and Technolgy(KAUST)Electrical Engineering and Mechanical [email protected]

180 DS13 Abstracts

MS70

Set-Valued Iteration Schemes for the Computationof Invariant Sets

Dynamically interesting invariant sets of dynamical sys-tems are typically approximated either by geometric con-struction or by fixed-point type iteration. We approachthis problem in a Banach space setting which allows toemploy Newton-type iterations that do not feature typicaldrawbacks of the aforementioned methods. Limitations tothe applicability initially arising from the technical setupcan be overcome using a covering approach that representsinvariant sets as (subsets of) unions of convex sets.

Mirko Hessel-von MoloInstitute for MathematicsUniversity of [email protected]

MS70

Deterministic Numerical Continuation for Stochas-tic Dynamical Systems

Continuation methods for deterministic dynamical systemshave been one of the most successful numerical tools in ap-plied dynamical systems theory. We show how to extendthese ideas to metastable equilibrium points of stochasticdifferential equations by combining results from probabil-ity, dynamical systems, numerical analysis, optimizationand control theory. The algorithm naturally augmentsclassical deterministic continuation and provides ellipsoidalconfidence neighborhoods and distances between.

Christian KuehnVienna University of [email protected]

MS70

Robust Optimal Control Problems: Extending Dif-ferential Approaches via Sets

In ”robust” control problem, two types of controls occurand, the user can choose only one of them whereas theother one is not known exactly (i.e. some uncertainty).This talk focuses on the analytical situation when the latterperturbations have an unknown or uncertain strategy. Itleads to non-standard (set-valued) initial value problemsfor states and controls. Finally we discuss the existence ofsolutions and their computability in principle.

Thomas LorenzGoethe University [email protected]

MS71

Flow Map Composition for Non-autonomous Dy-namical Systems

The flow map of a dynamical system plays a major rolein the computation of finite-time Lyapunov exponents, thePerron-Frobenius operator, and in uncertainty quantifica-tion using generalized polynomial chaos. However, theflow map calculation is expensive, both in computationtime and memory requirement. In this talk, we continueto develop the theory of flow map composition, wherebylong-time flow maps are constructed as the composition ofmultiple short-time flow maps. In addition, spectral inter-polation is introduced to dramatically reduce the memoryrequirement of storing intermediate flow maps. A care-

ful error analysis demonstrates the benefit of short-timecompositions. Long-time flow maps are characterized bysignificant stretching and folding of trajectories, whereasshort-time intermediate flow maps have less distortion andare more accurately represented by low-order basis func-tions. These ideas are illustrated on numerical examples.

Steven BruntonUniversity of [email protected]

MS71

Coherent Structure Identification Using Flow MapComposition and Spectral Interpolation

We propose an efficient method for computing the propa-gation of a probability density function through the long-time flow map associated with an uncertain velocity field.Uncertain initial conditions and parameters are both ad-dressed. We employ spectral representations for short-timeflow maps, and construct long-time flow maps by compos-ing them. The long-time flow map is used to computestochastic quantities, which are shown to be correlated tocoherent structures in the velocity field.

Dirk Martin LuchtenburgPrinceton [email protected]

MS71

Koopman Mode Analysis of Networks

Spectral analysis of a dynamical system’s associated Koop-man operator has proven fruitful in a number of areas.The so-called Koopman Mode analysis focuses on the pointspectrum (especially the eigenvalues on the unit circle),providing a “skeleton” of the dynamics, with little atten-tion given to the continuous part of the spectrum. Thistalk focuses on constructing the operators spectral measuredirectly from data allowing the analysis of the continuousspectrum.

Ryan MohrUniversity of California, Santa [email protected]

MS71

Coherent Sets from Data: Bifurcations, Braiding,and Predicting Critical Transitions

We discuss some results regarding identification of coher-ent sets, regions with long residence time, using a transferoperator approach, which are appropriate for systems of ar-bitrary time dependence defined by data, e.g., fluid flows.A topological analysis based on spatiotemporal braidingof coherent sets might be possible for analyzing chaos insuch systems. Furthermore, by considering changes in thetransfer operator modes, prediction of dramatic changes insystem behavior may be possible.

Shane D. RossVirginia TechEngineering Science and [email protected]

MS72

Mixed-mode Oscillations in the

DS13 Abstracts 181

Belouzov-Zhabotinsky Reaction

In stirred reactors, the Belousov-Zhabotinsky reaction dis-plays mixed mode oscillations in which small and large am-plitude oscillations alternate with one another. This lec-ture will describe studies of a six dimensional vector fieldformulated by Gyorgyi and Field as a model of the BZreaction which fits empirical data well. Extending resultsin the thesis of Chris Scheper, we use geometric singularperturbation theory to analyze mixed mode oscillations inthis model.

John GuckenheimerCornell [email protected]

MS72

Canard Cycles in Aircraft Ground Manoeuvres

We show that the sudden loss of lateral stability of a mid-size passenger aircraft turning on the ground is due to acanard explosion.

James RankinINRIA [email protected]

Mathieu DesrochesINRIA [email protected]

Bernd KrauskopfUniversity of AucklandDepartment of [email protected]

Mark LowenbergDept. of Aerospace EngineeringUniversity of [email protected]

MS72

Spike-adding Mechanisms in Transient Bursts

Dynamical systems tools are designed to explain the long-term bahaviour of a system, that is, what happens aftertransients have died out. In many applications, however, itis more important to understand the transient rather thanasymptotic behaviour. In this talk we employ standardtools from dynamical systems in order to analyse transientbursting behaviour. To illustrate these ideas, we use theexample of an excitable cell model that is subject to a briefperturbation.

Jakub NowackiTessellaAbingdon Science Park, [email protected]

Hinke M. OsingaUniversity of AucklandDepartment of [email protected]

Krasimira Tsaneva-AtanasovaDepartment of Engineering MathematicsUniversity of [email protected]

MS72

Canard- and Hopf-induced Mixed-mode Oscilla-tions in Pituitary Cells

It has been shown that large conductance potassium (BK)current tends to promote bursting in pituitary cells. Thisrequires fast activation of the BK current, otherwise it isinhibitory to bursting. In this work, we analyze a pituitarycell model to answer the question of why BK activationmust be fast to promote bursting. In particular, we showthat the bursting can arise from either canard dynamics orslow passage through a dynamic Hopf bifurcation.

Theodore VoUniversity of [email protected]

Joel TabakDept of Biological SciencesFlorida State [email protected]

Richard BertramDepartment of MathematicsFlorida State [email protected]

Martin WechselbergerUniversity of [email protected]

MS73

Iterated Birth and Death Markov Branching Pro-cesses as a Model of Irradiated Cancer Cell Survival

We solve, under realistic assumptions, the following prob-lem in radiation biology and oncology: finding the distri-bution of the number of tumor cells surviving fractionatedradiation. Based on birth and death Markov branchingprocess model of tumor cell population kinetics we find anexplicit formula for the distribution in question and iden-tify two of its limiting forms: the Poisson distribution andthe generalized Poisson distribution. We also estimate therate of convergence to the Poisson distribution.

Leonid G. HaninDepartment of MathematicsIdaho State [email protected]

MS73

Multiscale Stochastic Reaction-diffusion Algo-rithms Combining Markov Chain Models withSPDEs

In this talk, I will introduce a multiscale algorithm forstochastic simulation of reaction-diffusion processes. Thealgorithm is applicable to systems which include regionswith a few molecules and regions with a large number ofmolecules. A domain of interest is divided into two subsetswhere continuous-time Markov chain models and stochas-tic partial differential equations (SPDEs) can be respec-tively used. Several examples with simulation results willbe shown. This is a joint work with Radek Erban at theUniversity of Oxford.

Hye-Won KangOhio State UniversityMathematical Biosciences Institute

182 DS13 Abstracts

[email protected]

MS73

Multistage Carcinogenesis and Cancer Evolution asa Branching Process

Stochastic models of multistage carcinogenesis, cancer evo-lution at the cellular level, have played an important rolein the analysis of cancer epidemiology data since the 1950s.By being biologically-based, multistage models can be usedto test hypothesis about carcinogens mechanisms of actionand to gauge their effects on cancer risk. In this talk Iwill show how to analyze multistage carcinogenesis modelsas continuous branching processes and the advantages ofdoing so versus alternative approaches.

Rafael MezaUBC Centre for Disease ControlDivision of Mathematical [email protected]

MS73

HPV and Cervical Cancer: A Stochastic Model atTissue Level

Infection with the Human Papilloma Virus (HPV) is a pre-requisite for cervical cancer. While ∼ 80% of women getinfected during their lifetime, most clear the virus within2 years. If the infection persists, it can lead to malignantcancer. Various aspects of the carcinogenesis remain poorlyunderstood at the cellular level. We develop a stochasticmodel of the cervical epithelium, coupling the dynamics ofHPV infection to a multi-stage model of cancer evolution.

Marc D. RyserDepartment of Mathematics and StatisticsMcGill University, [email protected]

MS74

Uncertainty Quantification and Decisions inMarkovian Dynamics


Roger GhanemUniversity of Southern CaliforniaAerospace and Mechanical Engineering and [email protected]

MS74

Linking Diffusion Maps with Coarse-graining Com-plex System Dynamics


Ioannis KevrekedisPrinceton [email protected]

MS74

Patch Dynamics for Macroscale Modelling of Dif-

fusion in Heterogeneous Media


Anthony J. RobertsUniversity of [email protected]

MS74

Accurate Bifurcation Diagrams of an Agent-based Sociological Model Using Variance-reducedJacobian-vector Products


Giovanni SamaeyDepartment of Computer Science, K. U. [email protected]

MS75

Mesoscopic Structure and Social Aspects of HumanMobility

The individual movements of large numbers of people areimportant in many contexts, from urban planning to dis-ease spreading. Datasets that capture human mobility arenow available and many interesting features have been dis-covered, including the ultra-slow spatial growth of indi-vidual mobility. However, the detailed substructures andspatiotemporal flows of mobility the sets and sequencesof visited locations have not been well studied. I’ll dis-cuss an empirical project where we found that individualmobility is dominated by small groups of frequently vis-ited, dynamically close locations, forming primary habi-tats capturing typical daily activity, along with subsidiaryhabitats representing additional travel. These habitats donot correspond to typical contexts such as home or work.The temporal evolution of mobility within habitats, whichconstitutes most motion, is universal across habitats andexhibits scaling patterns both distinct from all previous ob-servations and unpredicted by current models. The delayto enter subsidiary habitats is a primary factor in the spa-tiotemporal growth of human travel. Interestingly, habi-tats correlate with non-mobility dynamics such as com-munication activity, implying that habitats may influenceprocesses such as information spreading and revealing newconnections between human mobility and social networks.

James BagrowEngineering Sciences and Applied MathematicsNorthwestern [email protected]

Yu-Ru LinCollege of Computer and Information ScienceNortheastern [email protected]

MS75

The English Language has a Self-similar,Positively-biased Emotional Spectrum

We show that the emotional content of individual Englishwords exhibits a spectrum with a strong positive bias,largely independent of word usage frequency. Our find-ings suggest a deep linguistic encoding of the pro-social,cooperative nature of people, and hold broadly across fourdiverse large-scale text corpora: Twitter, the New YorkTimes, Google Books, and music lyrics. Our Mechani-

DS13 Abstracts 183

cal Turk measurements for over 10,000 words statisticallyagree with but greatly expand upon previous, limited stud-ies.


Isabel KloumannDepartment of MathematicsCornell [email protected]


Kameron D. HarrisUniversity of [email protected]

Catherine A. BlissUniversity of VermontDepartment of Mathematics and [email protected]

MS75

Unraveling Daily Human Mobility Motifs

We uncover daily mobility patterns and identify the un-derlying mechanism responsible for the observed behavior.By using the concept of motifs from network theory, weshow that despite the existence of millions of possible net-works, only a few networks are present, following simplerules. Only 17 networks, called here motifs, are sufficientto capture up to 90% of the population in datasets obtainedfrom both surveys and anonymized mobile phone data fordifferent countries.

Marta Gonzalez, Christian Schneider, Vitaly BelikCivil and Environmental [email protected], [email protected], [email protected]

MS75

Revealing the Character of Cities Through Dataand Hedonometrics

We investigate how geographical location influences indi-vidual happiness, using a novel algorithm applied to wordfrequencies collected from Twitter messages. We exam-ine differences in word usage between US cities, and usingcensus data explain how happiness relates to underlyingphysical and social factors in those cities. Furthermore, weattempt to categorize cities in a data-driven way based ondifferences in word use and demographics.

Lewis MitchellThe University of VermontDepartment of Mathematics and [email protected]


Peter DoddsDepartment of Mathematics and StatisticsThe University of [email protected]

Morgan R. FrankUniversity of Vermont, Complex Systems [email protected]

MS76

Using Neural Mass Models and Bifurcation Theoryto Understand Transitions to Pathological Oscilla-tions in Neural Systems

Neural mass models (NMMs) are employed as a means ofcapturing the bulk properties of interacting populationsof neurons. The response of each population is governedby a differential equation. The equations are coupled to-gether according to the schematic structure of the modeland solved numerically. Bifurcation analysis can then beused to understand the range of solutions and the tran-sitions between them. We examined a NMM of corticaltissue to better understand focal-onset epilepsy.

Alex BlenkinsopDepartment of NeuroscienceUniversity of [email protected]

John TerryUniversity of [email protected]

MS76

Use of Mesoscale Models to Understand Data onSleep and Seizures, and to Investigate Options forSeizure Control

A method is presented for probabilistically tracking theevolution of measured electroencephalogram data in thesleep parameter space of a mean-field cortical model. Thisalgorithm is then applied to track the parameter evolutionof seizures.Extending the seizure applications, the effect on seizuredynamics of a control algorithm using a charge balancedoptogenetics actuator is studied. Optogenetics enable op-tical stimulation of neurons with high spatial and temporalresolution.

Vera DadokDepartment of Mechanical EngineeringUniversity of California, [email protected]

Prashanth Selvaraj, Andrew SzeriUniversity of California, [email protected], [email protected]

MS76

Mean Field Models of the EEG: Physiological Rel-evance and Mathematical Challenges

We will give a brief overview of a number of importantmean field approaches to modelling brain activity that havebeen applied with varying degrees of fidelity to articulatingthe genesis of rhythmic electroencephalographic activity inhealth and disease. This brief survey will conclude witha discussion of the mathematical challenges, particularly

184 DS13 Abstracts

the simulation, bifurcation analysis and parameter estima-tion, that these theories will need to negotiate in order toprogress as neurobiologically effective explanatory frame-works.

David LileySwinburne University of [email protected]

MS76

Bifurcation and Pattern Formation in a Mean-fieldModel of the Electroencephalogram

We study a model of the electrical potentials generated byexcitatory and inhibitory neuron populations in the cor-tex. The model takes the form of a system of semilinear,hyperbolic PDEs, that allow for oscillatory solutions andtravelling waves. We implemented the model in the open-source software PETSc, which allows for the continuationof equilibria and periodic orbits, and re-analyzed results byBojak & Liley on the onset of self-organised 40Hz oscilla-tions near a Hopf-Turing bifurcation.

Lennaert van Veen, Kevin R. [email protected], [email protected]

MS77

On the Maxwell-Bloch Equations with Non-zeroBoundary Conditions

The initial-boundary value problem for the Maxwell-Blochequations with non-zero fields at infinity is considered. Theinverse scattering transform is formulated and is used toinvestigate the behavior of the solutions.

Gino BiondiniState University of New York at BuffaloDepartment of [email protected]

MS77

Light Propagation in Lambda-configuration Meta-materials with Mixed Positive and Negative Re-fractive Index

We study numerically the propagation of two-color lightpulses through a metamaterial doped with active atomssuch that the carrier frequencies of the pulses are in res-onance with two atomic transitions in the Λ configura-tion and that one color propagates in the regime of posi-tive refraction and the other in the regime of negative re-fraction. In such a metamaterial, one resonant color oflight propagates with positive and the other with nega-tive group velocity. We investigate nonlinear interaction ofthese forward- and backward-propagating waves, and findself-trapped waves, counter-propagating radiation waves,and hot spots of medium excitation.

Alexander O. KorotkevichDept. of Mathematics & Statistics, University of NewMexicoL.D. Landau Institute for Theoretical Physics [email protected]

MS77

Dynamics of Light Propagating through Active Op-

tical Media

The Maxwell-Bloch equations describe resonant interactionbetween light and active optical media, whose many mech-anisms are captured by their lossless limit. They includerandom polarization switching in randomly prepared me-dia and light pulses slowed down to a fraction of the speedof light, solvable by the inverse-scattering transform. Anon-integrable variation of the Maxwell-Bloch equationsdescribes propagation of light through meta-materials withnegative and positive refractive indices for two resonantfrequencies of the light pulses.

Gregor KovacicRensselaer Polytechnic InstDept of Mathematical [email protected]

Katherine NewhallCourant Institute of Mathematical ScienceNew York [email protected]

Ethan AtkinsCourant [email protected]

Kathryn RasmussenMathematics DepartmentBrevard [email protected]

Alexander O. KorotkevichDept. of Mathematics & Statistics, University of NewMexicoL.D. Landau Institute for Theoretical Physics [email protected]


Gino BiondiniState University of New York at BuffaloDepartment of [email protected]

Ildar R. GabitovDepartment of Mathematics, University of [email protected]

MS77

On the Coupled Maxwell-Bloch Equations with In-homogeneous Broadening for a 3-level System

The initial value problem (IVP) for the propagation ofa pulse through a resonant 3-level optical medium canbe solved by Inverse Scattering. While the scatteringproblem is the same as for the coupled NLS, the timeevolution depends on asymptotic values of the materialpolarizability envelopes and is highly nontrivial. Thistalk will address the solution of the IVP for the coupledMaxwell-Bloch equations with inhomogeneous broadeningfor generic preparation of the medium.

Barbara PrinariUniversity of Colorado, Colorado SpringsUniversity of Salento, Lecce (Italy)

DS13 Abstracts 185

[email protected]

MS78

Hydrodynamic Mean-?eld Solutions of 1D Exclu-sion Processes with Spatially Varying HoppingRates


Thomas ChouUniversity of California, Los [email protected]

MS78

Novel Features in an Accelerated Exclusion ProcessTowards Modeling Transcription

Inspired by the cooperative speed-up observed in transcrib-ing RNA polymerases, we introduce distance-dependentinteractions in an accelerated exclusion process (AEP).Each particle moves to the neighboring site if vacant.Additionally, if reaching another cluster of particles, itcan kick up the frontmost particle in that cluster. Thesteady state of AEP shows a discontinuous transition, frombeing homogeneous (with augmented currents) to phase-segregated. More surprisingly, the current-density relationin the phase-segregated state is simply J = 1−ρ, indicatingthe particles (or holes) are moving at unit velocity despitethe inclusion of long-range interactions.

JiaJia DongDepartment of PhysicsBucknell [email protected]

Stefan KlumppMax Planck Institute of Colloids and Interfacesstefan klumpp [email protected]

R.K.P. ZiaVirginia TechIowa State [email protected]

MS78

Traffic Flow Model for Bio-Polymerization Pro-cesses

Bio-polymerization processes like transcription and trans-lation are central to a proper function of a cell. The speedat which the bio-polymer grows is affected both by num-ber of pauses of elongation machinery, as well their num-bers due to crowding effects. In order to quantify theseeffects in fast transcribing ribosome genes, we rigorouslyshow that a classical traffic flow model is a limit of meanoccupancy ODE model. We compare the simulation of thismodel to a stochastic model and evaluate the combined ef-fect of the polymerase density and the existence of pauseson transcription rate of ribosomal genes.

Tomas GedeonMontana State UniversityDept of Mathematical [email protected]

Lisa G. Davis, Jennifer Thorensen, Jakub GedeonMontana State [email protected], [email protected],

[email protected]

MS78

Random Hydrolysis Controls the Dynamic Insta-bility in Microtubules

One of the most fascinating phenomena associated with cy-toskeleton proteins is dynamic instability in microtubules,when these biopolymers can be found in growing or shrink-ing dynamic phases. Despite multiple efforts, mechanismsof this phenomenon are still not well understood. Here wepresent a microscopic stochastic model of dynamic instabil-ity which explicitly takes into account all relevant biochem-ical processes. It provides a comprehensive description ofthe dynamic instability of microtubules. Our theoreticalresults are supported by Monte Carlo simulations, and theyalso agree with all available experimental observations.

Anatoly B. KolomeiskyRice [email protected]

MS79

Lamprey Locomotion Driven by Non-linear MuscleMechanics and Work-dependent Deactivation

The swimming behavior observed in lampreys is the resultof the balance of forces from activated muscle, from theresponse of different tissues of the body and from reactionsof the surrounding fluid environment. Here we examinesome of the effects of nonlinear muscle mechanics and neu-ral activation on the forces generated along the body of theorganism. Implications of the force generation pattern onswimming efficiency and performance of the organism arediscussed.

Christina HamletTulane UniversityNew Orleans [email protected]

Lisa J. FauciTulane UniversityDepartment of [email protected]

Eric TytellTufts UniversityDepartment of [email protected]

MS79

Optimal Open- and Closed-loop Control of Anguil-liform Swimming

We study optimal control of an existing model of anquil-liform swimming developed by McMillen and Holmes inwhich the body is approximated by a finite number oflinked segments. We minimize a cost function that pe-nalizes both positive and negative work. We consider boththe open-loop problem in which muscle torques are speci-fied and the closed-loop problem in which muscle torquesdepend on the motion of the body perturbed by noise.

Tim KiemelUniv. of [email protected]

186 DS13 Abstracts

Kathleen HoffmanUniversity of Maryland Baltimore [email protected]

MS79

Lamprey Swimming, a Hydrodynamic Approach

We use a robotic lamprey to investigate the wake structureduring anguilliform swimming. 11 servomotors produce atraveling wave along the lamprey body. The waveform isbased on kinematic studies of living lamprey. PIV mea-surements show that a 2P structure dominates the wake.The phase-averaged surface pressure distribution along thecenterline of the robot increases toward the tail, indicat-ing that thrust is produced mainly at the tail. The phaserelationship between these signals is also examined.

Megan C. LeftwichMech. & Aerospace Eng.George Washington [email protected]

MS79

Strategies for Swimming: Explorations on the Be-haviour of a Neuro-musculo-mechanical Model ofthe Lamprey

Fish swim by generating waves of muscle activation thatpass down the body toward the tail. Such activation pro-duces traveling waves of lateral curvature, which developforward thrust from the surrounding water. Increasedswimming speed is brought about by increasing both thefrequency of the waves and the strength of muscle acti-vation. We use a combined model of the body in which arecently developed model for the muscle forces is employed,and coupled with forces due to the surrounding fluid. Weshow that over a range of ratios between the wave speedsof activation and curvature, the ratio that is observed ex-perimentally in the lamprey gives rise in the model to themaximum forward speed. This was true over a wide rangeof model parameters.

Tyler McMillanDepartment of MathematicsCalifornian State University at [email protected]

Thelma WilliamsDepartment of Mechanical and Aerospace EngineeringPrinceton University, Princeton, [email protected]

MS80

Stationary Co-dimension 1 Structures in the Func-tionalized Cahn-Hilliard Model

The functionalized Cahn-Hilliard equation appeared re-cently in the study of polymer-electrolyte membranes. Itgenerates an intriguing variety of evolving thin structures.Here, we focus on simple stationary structures and their bi-furcations: flat plates and spherical/cylindrical shells. Theexistence problem corresponds to constructing homoclinicsolutions in a perturbed integrable Hamiltonian system.The stability is established by a careful analysis of a (pro-jected) 4th-order operator in which two potential destabi-lization mechanisms - meandering and pearling - must be

controlled.

Arjen DoelmanMathematisch [email protected]

Keith PromislowMichigan State [email protected]

MS80

Stability of Multi-Bump, Blowup Solutions of theGinzburg-Landau Equation with Respect to Non-Radially Symmetric Perturbations

In this talk we study, the stability of radially symmetricblowup solutions of the Ginzburg-Landau equation withrespect to radially symmetric and non-radially symmetricperturbations. Upon writing the Ginzburg-Landau equa-tion as a small perturbation of the nonlinear Schrodingerequation, the existence of multi-bump blowup solutions, es-pecially of ring-like solutions, has already been established.So far, the stability of these blowup solutions had onlybeen examined numerically. We use Evans function tech-niques developed for perturbations of Hamiltonian systemsto study the stability of the ring-type solutions dependingon the parameters in the system.

Vivi RottschaferLeiden UniversityDeparment of [email protected]

Martin Van Der SchansLeiden [email protected]


MS80

Stability of Multiple Solutions in a Convection-diffusion-reaction PDE

In this talk we will discuss the stability of non-uniquesteady-state solutions of a time-dependent convection-diffusion-reaction PDE. Its stationary version can be recog-nized as an extended Bratu-model with damping. Depend-ing on the form of the reaction term, we can identify zero,one, two, or even infinitely many steady-states. Stabilityanalysis of the evolutionary PDE shows that only one ofthese solutions can be stable.

Paul A. ZegelingDept. of MathematicsUtrecht [email protected]

MS80

Unstable Spots in a FitzHugh-Nagumo System

In this talk, I will look at several destabilizing scenariosfor planar localized structures such as spots and stripesin a generalized FitzHugh-Nagumo equation. We are es-pecially interested in the bifurcation of a stationary spotinto a travelling spot. Using formal analysis and the nu-merical continuation package AUTO-07p, we determine the

DS13 Abstracts 187

location of this pitchfork bifurcation, its criticality and theshape and speed of the bifurcating traveling spot. This isjoint work with B. Sandstede.

Peter van HeijsterDepartment of Mathematics and StatisticsBoston [email protected]


MS81

A Novel Model for Collective Behavior in Groupsof Predators

In this work, we present a novel model of a multi-agentsystem inspired by the phenomenon of bat swarming. Themodel is unique in the coupling between agents, interactionmodalities, and communication mechanisms. We define anorder parameter based on navigation and foraging successto explore the emergence of collective behavior.

Yuan LinVirginia Polytechnic Institute and State [email protected]

Nicole [email protected]

MS81

Evolution of Networks of Multi-agent Systems onLow-dimensional Manifolds

In this work, we use a nonlinear dimensionality-reductiontechnique called Isomap to infer the complexity of anetworked multi-agent system. Using image streams ofinteracting-particle models as input to the Isomap algo-rithm, the dimensionality of the resulting submanifoldis used to determine the degree of alignment betweenagents. We further exploit local linearity of the input high-dimensional manifold to detect phase transitions in collec-tive motion. Finally, we validate this approach on realdatasets comprising raw videos of zebrafish schools.

Sachit ButailUniversity of MarylandDepartment of Aerospace [email protected]

Nicole AbaidVirginia Polytechnic Institute and State [email protected]

Erik BolltClarkson [email protected]

Maurizio PorfiriDept. of Mechanical, Aerospace and ManufacturingEngineeringPolytechnic [email protected]

MS81

Dynamics of Delocalized Consensus Formation

Many systems in Science and Engineering need to pro-cess information collectively, with examples ranging fromneural networks, to biological swarms, and decentralizedsensor nets. In this talk I present a series of analyticallytractable network models of decission dynamics that areused to identify beneficial and detrimental factors in col-lective decission-making. In particular, I will show thatalready very simple models make predictions that can beverified in experiments with humans and animals.

Thilo GrossUniversity of Bristol, [email protected]

MS81

Computation from Adaptive Synchronization

It is generally accepted that the brain transmit and pro-cess information by means of synchronization. For in-stance, neural assemblies are known to organize theirdynamics in a balance between synchronization and de-synchronization, and modifications of such balance havebeen associated with a number of neurological illnesses, in-cluding schizophrenia and Alzheimers disease. Yet, howto conciliate computation and synchronization, when thelatter can be seen as a destruction of information, is stillan open problem. Here, we present a framework for thespontaneous emergence of computation from adaptive syn-chronization of networked dynamical systems. The funda-mentals are nonlinear elements, interacting in a directedgraph via a coupling that adapts itself to the synchro-nization level between two input signals. We demonstratehow these units can emulate different Boolean logics, andperform any computational task in a Turing sense, eachspecific operation being associated with a given network’smotif.

Massimiliano ZaninTechnical University of [email protected]

MS82

Attractors Near Grazing-sliding Bifurcations

We will present a method of analysis of grazing-slidingbifurcation scenarios, that may lead to the birth of mul-tiple attractors from a single attractor in three dimen-sional Filippov type flows, by appropriate reduction to one-dimensional discontinuous maps. Three, qualitatively dif-ferent, scenarios will be presented. A constructed exampleof a Filippov type flow, displaying the analysed cases, willbe shown. We will then verify the presence of attractors,using the model example, numerically.

Piotr KowalczykDept. Engineering MathematicsUniversity of [email protected]

Paul Glendinningthe University of [email protected]

Arne NordmarkDepartment of MechanicsRoyal Institute of Technology

188 DS13 Abstracts

[email protected]

MS82

Bifurcation Analysis of an Intermittent ControlModel During Human Quiet Stance: A PossibleMechanism of Postural Sway

Ground reaction force during human quiet stance is knownto be modulated with the cardiac cycle through hemody-namics, inducing a tiny periodic disturbance torque to theankle joint. Can it be a major source of perturbation induc-ing postural sway? Here we consider postural sway dynam-ics of an inverted pendulum with an intermittent controlstrategy, and show that, based on a bifurcation analysis,the model with the hemodynamic perturbation can exhibithuman-like postural sway.

Taishin Nomura, Yasuyuki Suzuki, Tomohisa Yamamoto,Ken KiyonoOsaka University, [email protected], [email protected],[email protected],[email protected]

Pietro MorassoItalian Institute of Technology, [email protected]

MS82

Dynamics Near Incomplete Chattering

The dynamics of mechanical models with impact is consid-ered. In particular, the dynamics for trajectories that areclose to the border between complete and incomplete chat-tering is studied. In the single degree of freedom situation,a limit mapping is derived as the border is approached, thatapart from scaling only depends on the coefficient of resti-tution. The multi-degree of freedom case is also discussed.

Arne NordmarkDepartment of MechanicsRoyal Institute of [email protected]

MS82

Transient Dynamics in Impacting Systems

It is well known that mechanical systems with impacts canundergo chattering, a large number or even an infinite num-ber of impacts in finite time. There are successful attemptsat trying to explain the local behaviour of chattering butglobal analysis is still somewhat missing. Here we will dis-cuss the global dynamics of an impact oscillator that canundergo chattering through analysis of the transient dy-namics as the position of the impacting surface is varied.

Petri T. PiiroinenSchool of Mathematics, Statistics and AppliedMathematicsNational University of Ireland, [email protected]

Arne NordmarkDepartment of MechanicsRoyal Institute of [email protected]

David ChillingworthMathematicsUniversity of [email protected]

MS83

A Deterministic Perspective on Stochastic Ther-modynamics: Local Equilibrium and InformationTheory

Stochastic thermodynamics (ST) extends equilibrium ther-modynamics to treat nonequilibrium processes on muchsmaller, so-called mesoscopic scales. Its consistency relieson local equilibrium (LE). The most prominent results ofST are nonequilibrium fluctuation relations (cf. Rondoni’stalk). However, LE is a strong assumption which does notalways apply. This is the case for systems without a clearseparation of scales (cf. Lucarini’s talk) or strongly dissi-pative systems (cf. Swift’s talk). In my talk, I will presenta deterministic approach to ST and discuss routes towardsa dynamical picture of LE.

Bernhard AltanerMax-Planck-Insitute for Dynamics and [email protected]

Jurgen VollmerMax Planck Institute for Dynamics and [email protected]

MS83

Statistical Physics of the Climate System

The investigation of the climate system is one of the grandchallenges of contemporary science. Such a problem isgaining more and more relevance as exoplanets are beingdiscovered at an accelerating rate and rather exotic atmo-spheric circulations are being conjectured, due to the vastvariety of possible astronomical and astrophysical config-urations. In this contribution we will discuss how non-equilibrium statistical mechanics allows framing in a rig-orous and efficient way classical problems of climate sci-ence such as the understanding of the climatic responseto forcings of general nature and the parametrization ofunresolved processes.

Valerio LucariniUniversity of Reading, Reading, [email protected]

MS83

Gravity-Wave Detectors and Nonequilibrium Sta-tistical Physics of Very Cold Systems

The detection of gravitational waves requires exceedinglyaccurate measurement tools, capable of recording micro-scopic fluctuations in macroscopic objects. Recently, thesetools have been found to operate in non-equilibrium condi-tions, thus allowing direct tests of the non-equilibrium fluc-tuation relations developed in the past two decades. Wewill review the relevant well established results, and wewill present novel analysis concerning response and non-equilibrium temperature relations.

Lamberto RondoniPolitecnico di Torino, Torino, [email protected]

DS13 Abstracts 189

MS83

Phase Coexistence and Surface Tension in VibratedGranular Fluids

We describe experiments and simulations carried out toinvestigate phase separation in a vibrated, dry granularsystem. The dynamics is found to be controlled by cur-vature driven diffusion, which suggests the presence of aneffective surface tension. We find behaviour consistent withLaplace’s equation and detailed measurements of the pres-sure tensor in the interfacial region show that the surfacetension results predominantly from an anisotropy in thekinetic energy part alone.

Michael SwiftThe University of Nottingham, Nottingham, [email protected]

MS84

Bayesian Data Assimilation with Optimal Maps

We develop a novel, map-based schemes to sequential dataassimilation, i.e., nonlinear filtering and smoothing. Onescheme involves pushing forward a fixed reference mea-sure to each filtered state distribution, while an alternativescheme computes maps that push forward the filtering dis-tribution from one stage to the other. The main advantageis that the map approach inherently avoids issues of sampleimpoverishment, since it explicitly represents the posterioras the pushforward of a reference measure, rather than witha particular set of samples. The computational complexityof our algorithm is comparable to state-of-the-art parti-cle filters. We demonstrate the efficiency and accuracy ofthe map approach via data assimilation in several canon-ical dynamical models, e.g., the Lorenz-63 and Lorenz-96systems.

Tarek El MoselhyMassachusetts Institute of [email protected]

MS84

Estimating Global Electric and Magnetic Fields inPlasma Experiments and Particle-in-Cell Codes inthe presence of noise for the Purpose of PredictingIncipient Magnetic Reconnection

Diagnosing magnetic reconnection from experimental data,from particle-in-cell (PIC) simulations, or from space ob-servations involves making measurements, which are eas-ily obtained in PIC data, sparse in experiments and verysparse in observations. The latter two measurements havehigh noise levels and the PIC data has inherent PIC noise.We have developed methods of estimating the electric andmagnetic fields and associated global structures such as sta-ble and unstable manifolds to diagnose reconnection andincipient reconnection.

John M. FinnLos Alamos National [email protected]

MS84

Propagating Uncertainty About Gas EOS to Per-formance Bounds for an Ideal Gun

For any strongly connected directed graph, a particularset of branching probabilities maximizes the entropy rateof the resulting Markov process. Calculating those proba-

bilities can yield probability measures for constrained setsof functions. Curiously, the calculation is equivalent to oneof Shannon’s early Information Theory results. I motivatethe problem by the challenge of characterizing uncertaintyabout the performance of a gas driven gun and comparethat to the application Shannon addressed.

Andrew M. FraserLos Alamos National [email protected]

MS84

Coarse-graining Emergent Behavior from ComplexModels

Mathematical models are often extremely complex and in-volve many unknown parameters; however, the collectivebehavior of the system is often surprisingly comprehensi-ble. We consider the manifold of all possible predictionsin data space and find that it is typically bounded witha hierarchy of widths. Long directions describe emergentbehavior while narrow directions correspond to irrelevantdetails. Approximating the model manifold by its bound-ary coarse-grains away the microscopic details producingmodels of emergent behavior.

Mark K. TranstrumCornell [email protected]

MS85

Surfactant-induced Gradients inthe Three-dimensional Belousov-Zhabotinsky Re-action

Experimentally, scroll wave dynamics is often studied byoptical tomography in the Belousov-Zhabotinsky reaction,which produces CO2 as an undesired product. Addition ofsmall concentrations of a surfactant to the reaction mediumsuppresses or retards bubble formation. We show that inclosed reactors even these low concentrations of surfactantsare sufficient to generate vertical gradients of excitability.In reactors open to the atmosphere such gradients can beavoided. The gradients induce a twist on vertically ori-ented scroll waves, while a twist is absent in scroll wavesin a gradient-free medium. These findings are reproducedby a numerical study, using an extended Oregonator thataccounts for CO2 production and for its advection againstthe direction of gravity.

Markus BarPhysikalisch-Technische BundesanstaltFachbereich Mathematische Modellierung [email protected]


Dennis KupitzInstitut of Experimental [email protected]

Marcus HauserInstitute of Experimental [email protected]

190 DS13 Abstracts

MS85

Geometrically Constrained Wave Propagation inExcitable Media

It is well-known that domain size may strongly influ-ence dynamics and stability of travelling excitation waves.I report on theoretical and experimental results aboutscroll ring evolution constrained to thin layers with no-flux conditions imposed at the boundaries. Results includeboundary-induced suppression of negative line-tension in-stability accompanied by formation of stable autonomouspacemakers. Experiments were performed in thin trans-parent layers of the Belousov-Zhabotinsky reaction.

Harald EngelInstitut fur Theoretische Physik, Technische UniversitatBer10623 Berlin, [email protected]

MS85

Twists of Opposite Handedness on a Scroll Wave

The interaction of a gradient of excitability and a scrollwave of the Belousov-Zhabotinsky reaction oriented (al-most) perpendicular to the vertical gradient is studied. Fil-aments with a component parallel to the gradient twist,whereas scrolls with U-shaped filaments develop twistsfrom both ends of the filaments. These filaments display apair of twists of opposite handedness, which are separatedby a nodal plane where the filament remained untwisted.The experimental findings were reproduced by numericalsimulations.

Marcus HauserInstitute of Experimental [email protected]

Patricia DahmlowInstitute of Experimental PhysicsOtto-von-Guericke University [email protected]


Markus BarPhysikalisch-Technische BundesanstaltFachbereich Mathematische Modellierung [email protected]

MS86

Stability Analysis of Flock Rings for 2nd OrderModels in Swarming

In this work we consider second order models in swarm-ing in which individuals interact pairwise with a power-lawrepulsive-attractive potentials. We study the stability forflock ring solutions and we show how the stability of thesesolutions is related to the stability of a first order model. Inunstable situations it is also possible to observe formationof clusters and fat rings.

Daniel BalagueDepartament de Matematiques

Universitat Autnoma de [email protected]

Giacomo AlbiDipartimento di Matematica e InformaticaUniversita di [email protected]

Jose CarrilloDepartment of MathematicsImperial College [email protected]

James von BrechtUniversity of California, Los [email protected]

MS86

Instability and Bifurcation in a Trend DependingPrice Formation Model

A model for the formation of prices proposed by Lasry-Lions presents the evolution of such prices as a motion of afree boundary in a nonlinear parabolic problem. Its anal-ysis has received a lot of attention: the dynamics show asmooth evolution into a stable time-independent price. In-spired by the older work by Guidotti-Merino on the appear-ance of stable oscillations in a thermal control problem, wemodify the model in order to produce a Hopf bifurcationand existence of stable periodic solutions.

Maria Del Mar GonzalezUniversitat Politecnica de [email protected]

Maria GualdaniThe University of Texas at [email protected]

Joan Sola-MoralesUniversitat Politecnicade [email protected]

MS86

Computing Stationary States of Kinetic SwarmingModels

We consider a second-order self-propelled interacting par-ticle system, which has been frequently used to model com-plex behavior of swarms such as fish schools or birds flocks.We present recent advances in the explicit computation ofparticular solutions of the associated kinetic equation, suchas flocks and rotating mills. For so-called Quasi-Morse po-tentials, such density profiles can be expressed in terms ofa linear combination of special functions (in 2D and 3D).

Stephan MartinDepartment of MathematicsImperial College, [email protected]

MS86

Smoothing Transformations and Wealth Distribu-tions

We discuss Kac-like kinetic equations modeling wealth dis-tribution in simplified economies. Our models are derived

DS13 Abstracts 191

from ”microscopic” descriptions, in which wealth is ex-changed between agents in binary trades. Unlike the ki-netic energy in the original Kac equation, wealth is con-served only in the statistical mean. Extending McKean’sprobabilistic approach, we identify the Pareto-Index of thestationary state and the rate of convergence to equilibriumin terms of the model parameters.

Daniel MatthesDepartment of MathematicsTechnische Universitaet [email protected]

Federico BassettiUniversita di PaviaDipartimento di [email protected]

MS87

Modeling the Host Response to Inhalation Anthrax

Bacillus anthracis, the causative agent of anthrax, can ex-ist in the form of highly robust spores, thus making it apotential bio-terror threat. Once inhaled, the spores cangerminate into vegetative bacteria capable of quick repli-cation, leading to progressive disease and death. This pre-sentation discusses ongoing work on the development ofmathematical models that explore the host response to in-halation anthrax and provide insight into the mechanismsthat drive the risk of disease.

Judy DayUniversity of [email protected]

MS87

Innate Immune Response in Healthy and Immuno-compromised Host

The innate immune response to bacterial infection in a tis-sue compartment is modeled using an axiomatic approach,resulting in a three dimensional ODE system that describesthe dynamics of bacteria, neutrophils and G-CSF (the neu-trophils growth factor) in the site of infection. The mod-eling provide insights into the importance of killing mech-anisms other then the neutrophils. Moreover, we suggestan interplay between the concentrations of macrophages inthe tissue and neutrophil concentration in the blood.

Roy MalkaThe Weizmann InstituteApplied Math & Computer SciRoy [email protected]

MS87

Systems Biology of the Pulmonary Infection Pro-cess in Humans

We have developed the capability to non-invasively ac-quire aerosolized droplets of alveolar lining fluid (AALF)from the human lung. The droplets can contain pathogensand pathogen secreted ligands. The droplets also containbiomolecules from the host airway. Using AALF time serieswe have begun to investigated two avenues. Our primaryinterest is to predict which patients will progress to developpneumonia in the 72 hours prior to the manifestation ofclinical symptoms. Our secondary interest is to develop asound analytic framework from which we can regress early

treatment gains.



MS88

Clock-Driven Intermittent Controller and ModelBased Predicitve Controller for Human BalancingModels

Stabilizability of unstable equilibria in the presence of re-flex delay is investigated, such as stick balancing at the fin-gertip or postural sway during quiet standing. Two types ofcontrol concepts are investigated with respect to the criticalreflex delay, for which stable balancing is possible: (1) theact-and-wait controller is a special version of clock-drivenintermittent controllers; (2) the finite spectrum assignmentapproach is a kind of model based predictive feedback con-troller.

Tamas InspergerBudapest University of Technology and EconomicsDepartment of Applied [email protected]

John MiltonClaremont [email protected]

MS88

Intermittent Open Loop Control in Humans: Canthe Hypothesis be Tested?

Intermittent open loop control, otherwise known as serialballistic control, has been proposed repeatedly during thelast 60 years as a paradigm for human motor control. Inthe absence of rigorous, model based investigation and keyexperimental tests, this question has remained open. Herewe present recent model based experimental results sup-porting the case that sustained human control is serial bal-listic in nature and we consider explanations of why serialballistic control is relevant.

Ian LoramManchester Metropolitan [email protected]

Peter GawthropUniversity of Glasgow, UK &University of Melbourne, [email protected]

Henrik GolleeUniversity of Glasgow, [email protected]

Martin LakieUniversity of Birmingham, [email protected]

Cornelis van de Kamp

192 DS13 Abstracts

Manchester Metropolitan University, [email protected]

MS88

Evidence for Continuous Versus Intermittent Con-trol Mechanisms Contributing to Control of Hu-man Upright Stance

Controversy exists regarding whether human balance con-trol is regulated using a continuous feedback mecha-nism versus intermittent control mechanism. Several re-cent studies present experimental results that purport todemonstrate the contribution of intermittent control. Weshow that all these experimental results are in good agree-ment with a simple continuous feedback model that hasbeen used before to describe spontaneous sway propertiesof healthy young and elderly subjects as well as responsesto various external perturbations.

Robert PeterkaOregon Health & Science [email protected]

Christoph MaurerDepartment of NeurologyUniversity of [email protected]

MS88

An Intermittent Control of a Double Inverted Pen-dulum: Roles of Hip Motions Examined with Hu-man Postural Sway

Human upright quiet standing is stabilized by neural feed-back control with a relatively large transfer delay. To bet-ter understand the neural strategy for stabilization, we con-sidered dynamics of a double inverted pendulum modelwith an intermittent feedback controller. In-phase andanti-phase coordination between hip and ankle joints inthe model was compared with those in human. We thendiscuss roles played by hip joint motion during human quietstance.

Yasuyuki Suzuki, Taishin NomuraOsaka University, [email protected], [email protected]

Maura CasadioUniversity of GenoaDept. of Informatics, Systems, [email protected]

Pietro MorassoFondazione Istituto Italiano di TecnologiaRBCS [email protected]

MS89

Modeling Stochastic Neural Dynamics: Ap-proaches and Mathematical Issues

This talk will provide an overview of several approaches tostudying stochastic dynamics of neuronal networks, high-lighting and comparing approaches that will appear inother talks of the minisymposium while placing these ina broader context. Issues discussed will include choices ofrandom graph models, when a random graph is unneces-sary or inappropriate, and models for stochastic processes

on the nodes. A particular focus will be on mathematicalapproaches to analyzing the network dynamics.

Janet BestThe Ohio State UniversityDepartment of [email protected]

MS89

Interaction of Biochemical and Neural Networks inthe Brain

The standard electrophysiological perspective is that thebrain consists of networks of neurons that influence eachother through the biochemistry of neurotransmitter syn-thesis, release, and reuptake, viewing biochemistry as sim-ply a means of neuron-to-neuron communication. How-ever, many groups of neurons distantly release diffusingneurotransmitters that alter target biochemistry: the elec-trophysiology is the means by which the neurons projectbiochemical changes over long distances. The dynamics ofinteracting biochemical and electrophysiological networksprovide interesting mathematical challenges.

Michael ReedDuke [email protected]

Janet BestThe Ohio State UniversityDepartment of [email protected]

H Frederik NijhoutDuke [email protected]

MS89

Optimal Reduction of Complexity for Ornstein-Uhlenbeck Processes on Random Graphs

Extending Schmandt and Galan’s stochastic shielding ap-proximation, we consider the optimal complexity reducingmapping from a stochastic process on a graph to an approx-imate process on a smaller sample space, as determined bythe choice of a particular measurement functional on thegraph. We quantify the error introduced by the approxima-tion and provide an analytical justification for the method.We focus on the case of ion channel state partitioning intoconducting versus nonconducting states.

Deena [email protected]

MS89

Jigsaw Percolation: Which Networks Can Solve aPuzzle?

Jigsaw percolation is a process with the following dy-namics: groups of individuals merge if they are directlyconnected on an underlying social network, and if theyhave complementary information, i.e. compatible “puz-zle pieces’ which are connected via an auxiliary network.We analyze the probability of a total population merger,where a puzzle network is given and the social network is anErdos-Renyi random network with given edge probability

DS13 Abstracts 193

p.

David SivakoffMathematics DepartmentDuke [email protected]

MS90

Subdiffusive Fractional Equations with Space-dependent Anomalous Exponents

We show that subdiffusive fractional equations are notstructurally stable with respect to spatial perturbations tothe anomalous exponent. To rectify this problem we pro-pose the inclusion of the random death process into therandom walk scheme from which we arrive at the modi-fied fractional master equation. We analyze the asymp-totic behavior of this equation, both analytically and byMonte Carlo simulation, and apply it to the problem ofmorphogen gradient formation.

Sergei FedotovSchool of MathematicsUniversity of Manchester, [email protected]

MS90

Propagation of Fronts in Subdiffusive Media

We consider two kinds of fronts in systems with subdiffu-sion, reaction fronts and fronts of phase transitions. For theanalysis of reaction fronts, we use exactly solvable modelswith piecewise linear reaction functions. For fronts be-tween stable states, a drastic difference from the case ofnormal diffusion is revealed. Exact solutions correspond-ing to propagating phase transition fronts are also found,and their transverse instability is investigated.

Alexander NepomnyashchyTechnionIsrael Institute of [email protected]

Vladimir A. VolpertNorthwestern [email protected]

Yulia Kanevsky, Mohammad Abu HamedTechnion - Israel Institute of [email protected],[email protected]

MS90

Models and Tests for Anomalous Diffusion inCrowded Environment

Many experiments on the motion of particles in crowdedenvironments hint towards anomalous diffusion, mostlysubdiffusion. The nature of this subdiffusion can be quitediverse, and therefore needs for description within theoret-ical models based on different physical assumptions. Thedifference between time-inhomogeneous, non-ergodic mod-els and ergodic ones is deeply rooted in the thermodynam-ics of the corresponding processes, and it can be done eitherby running a test for ergodicity or a one for time homogene-ity. The distinction within the ergodic class can be basedon specific tests of homogeneity of filling of the space bythe corresponding trajectory and will be discussed in some

detail based on analytical and numerical examples.

Igor SokolovInstitut fuer PhysikHumboldt-Universitaet zu [email protected]

MS90

Weakly Nonlinear Analysis of the SuperdiffusiveBrusselator Model near a Codimension-two Turing-Hopf Bifurcation Point

A weakly nonlinear analysis is performed near acodimension-two Turing-Hopf point of the superdiffusiveBrusselator model in one spatial dimension. Two coupledamplitude equations describing the slow time evolution ofTuring and Hopf modes are derived. The dependence ofstability criteria of pure Turing, pure Hopf, and mixedmode solutions to long-wave perturbations on the anoma-lous diffusion exponents is discussed and compared to reg-ular diffusion.

Justin TzouIsrael Institute of Technology, Haifa, [email protected]

MS91

Nonautonomous Control of Invariant Manifolds

It is well-known that the temporal evolution of stable andunstable manifolds play a significant role in transport innonautonomous dynamical systems. As a first step towardsunderstanding how to control such manifolds, this talkaddresses the control problem of determining the nonau-tonomous velocity perturbation in two dimensions requiredto ensure that a one-dimensional heteroclinic manifoldsplits into stable and unstable manifolds whose primarysegments lie along specified time-varying curves in space.

Sanjeeva BalasuriyaConnecticut CollegeDepartment of [email protected]


MS91

A Stable Principle Manifold of a Separable Attrac-tor of the Nonautonomous Chaotic Beam System

An elastic beam subject to moving contact loads modelsexternal forcing of fluids in internal ship tanks. The mod-eling PDE has chaotic solutions with an attractor with adecomposable form that identifies dimensionality reductionthat encapsulates a Cartesian product, of a principle man-ifold corresponding to spatial regularity against a tempo-ral low-dimensional chaotic attractor at a fixed site on thebeam. The principle manifold serves to translate complexlow-dimensional information at one site to other sites.

Erik Bollt, Joseph SkufcaClarkson [email protected], [email protected]

194 DS13 Abstracts

MS91

Finite-Size Lyapunov Exponents (FSLE) and La-grangian Coherent Structures

Finite-Size Lyapunov Exponents (FSLE) have proven tobe effective indicators of hyperbolic Lagrangian CoherentStructures (LCS) in dynamical systems. However, comput-ing FSLE involves integration of different trajectories overdifferent time intervals, thus an exact mathematical con-nection between FSLE and LCS has been unknown. Herewe establish such a connection, which turns FSLE from aheuristic indicator into a rigorous LCS detection tool un-der certain conditions. We illustrate our results on simpleunsteady flow examples.

Daniel KarraschETH Zurich, [email protected]


MS91

Invariant Manifolds in Non-autonomous Equations

Economic models often lead to deep mathematical prob-lems. For example, classical solutions of economic growthmodels induce implicit, non-autonomous differential equa-tions, that are supplemented by transversality conditions.From a certain perspective, it is possible to relate the solu-tions of these equations to the existence of stable manifolds.Time dependence arises whenever models include discountfactors. We explore the existence of invariant manifolds inthis context and its relation to non-autonomous Hamilton-Jacobi problems.

Hector E. LomeliInstituto Tecnologico Autonomo De Mexico (ITAM)University of Texas at [email protected]

MS92

Plankton Bloom Front Meets Chain of Vortices ina Flow

Plankton blooms, particularly harmful algal blooms, canbe described by excitable systems. We study the impact ofa laminar one-dimensional flow as well as chain of vorticeson diffusion fronts which develop from a phytoplankton-zooplankton system. We discuss the emergence of differentplankton patterns depending on the different growth ratesof the species, the relation between the front velocity, themean flow velocity and the strength of the vortices.


MS92

A Chemical Front in the Faraday Flow

We investigate the transport in a turbulent quasi twodi-mensional laboratory flow induced by capillary Faradaywaves on a thin fluid layer. In experiments with an ex-citable autocatalytic chemical reaction in this flow, prop-agating chemical waves with a highly wrinkled front have

been observed. These observations demand for a detailedstudy of the underlying advective transport. We first char-acterize the vortex patterns in the flow in the Eulerianframe and relate them to the geometric pattern of the Fara-day waves. In a second part, we compute Lagrangian co-herent structures (LCS) that determine the spatiotemporalmixing patterns. Simultaneous experimental measurementof the velocity fields and the chemical concentration allowfor a superposition of the LCS onto the concentration field.This reveals that the LCS shape the advancing reactionfronts.

Alexandra Von KamekeFacultad de FisicasUniv. de Santiago de [email protected]

Florian HuhnInstitute for Mechanical SystemsETH [email protected]

Vicente Perez-Munuzuri, Alberto P. MunuzuriFaculty of PhysicsUniversity of Santiago de Compostela, [email protected],[email protected]


MS92

Pinning and Invariant Barriers in Advection-reaction-diffusion Systems

Invariant manifolds are important barriers to passive trac-ers in 2D time-independent and time-periodic flows. Al-though these manifolds are no longer defined for time-aperiodic flows, the past decade of research has demon-strated the significance of finite-time-lyapunov-exponents(FTLE) and lagrangian coherent structures (LCS). Re-cently barriers to front-propagation in (time-independentand time-periodic) fluid flows have been identified - socalled burning invariant manifolds (BIMs). We define ananalog of the FTLE for front-propagation in time-aperiodicflows using a dimension reduction. This type of analysismay find application in the analysis of oceanic planktonblooms, turbulent combustion, and industrial chemistry.

John R. MahoneyUniversity of California, [email protected]

MS92

Experimental Studies of Barriers to Front Propa-gation in Vortex-dominated Flows

We present experiments on the behavior of propagating re-action fronts in laminar fluid flows. This is an issue withapplications to a wide range of systems including combus-tion dynamics in flows with chaotic advection, microfluidicchemical reactors, and blooms of phytoplankton and algaein the oceans. To analyze and predict the behavior of thefronts, we generalize tools developed to describe passivemixing. In particular, the concept of an invariant mani-fold is expanded to account for reactive burning. ”Burn-ing invariant manifolds” (BIMs) are defined in a three-dimensional phase space. When projected into two spa-

DS13 Abstracts 195

tial dimensions, these BIMs provide barriers that retardthe motion of reaction fronts. Unlike invariant manifoldsfor passive transport, however, the BIMs are barriers forfront propagation in one direction only. These ideas aretested and illustrated experimentally in a chain of alter-nating vortices and an extended, spatially-random patternof vortices.

Thomas H. SolomonDepartment of Physics & AstronomyBucknell [email protected]

MS93

Transport and Flow in Complex Networks: Cas-cading Overload Failures in Networks with Dis-tributed Flows

In complex information or infrastructure networks, evensmall localized disruptions can give rise to congestion,large-scale correlated failures, or cascades, – a critical vul-nerability of these systems. Here, we study cascades ofoverload failures for distributed flows in spatial and non-spatial random graphs, and in empirical networks (inter-net and power grid). We review and investigate a few re-cently proposed schemes to mitigate such failures (e.g., pre-emptive node/edge removal, edge weighting, and assigningexcess capacities).

Gyorgy KornissDepartment of Physics, [email protected]

Andrea Asztalos, Sameet Sreenivasan, [email protected], [email protected],[email protected]

MS93

Walking and Searching in Time-Varying Networks

We study random walks in time varying networks consider-ing the regime of time-scale mixing. We derive analyticallythe stationary state and the mean first passage time of suchprocesses. The findings show striking differences with re-spect to the well-known results obtained in quenched andannealed networks, emphasizing the effects of dynamicalconnectivity patterns in the definition of proper strategiesfor search, retrieval and diffusion processes in time-varyingnetworks.

Nicola PerraNortheastern UniversityDepartment of [email protected]

MS93

Predicting Traffic Changes in the Wake of Geo-Localized Damages in Large-Scale TransportationNetworks

Traffic flows obey a path-cost minimization principle, gen-erating a heterogeneous use of network paths. Validatedon a US highway transportation data-set we present anovel method for computing network flows using the ra-diation law [F. Simini et.al., Nature 484, 96 (2012)] anda range-limited, weighted betweenness centrality measure

[M. Ercsey-Ravasz et.al. PhysRevE 85, 066103 (2012)].We then use this method to quantify the non-local effectsof geo-localized damages in the US highway transportationnetwork.

Yihui RenDepartment of Physics and iCeNSAUniversity of Notre [email protected]

Maria Ercsey-RavaszFaculty of PhysicsBabes-Bolyai University, [email protected]

Zoltan ToroczkaiUniversity of [email protected]

MS93

Power Grid Vulnerability to Geographically Corre-lated Failures

We consider line outages in the power grid, which arecaused by a natural disaster or a large-scale attack. Wepresent a model of such geographically correlated failures,investigate its properties, and show that it differs frommodels used to analyze cascades in the power grid. Weshow how to identify the most vulnerable locations in thegrid and perform extensive numerical experiments withgrid data to investigate the various effects of geographi-cally correlated outages.

Gil ZussmanColumbia UniversityDepartment of Electrical [email protected]

MS94

Population Dynamics and Preferential Segregation

It is well-know that particles segregate in turbulent flows.If, however particles of different Stokes number react witheach other, segregation of particles into different spatial re-gions may have a dramatic effect on population dynamics.We present first results on this topic by qualitative analysisand simple 2D numerical modeling.

Markus AbelUniversity of [email protected]

MS94

Interaction of Droplets and Turbulence inRayleigh-Benard Convection

Responses of a droplet ensemble during an entrainment andmixing process at the edge of a cloud are investigated bymeans of three-dimensional direct numerical simulations.We combine the Eulerian description of the turbulent ve-locity, temperature and vapor content fields with a La-grangian ensemble of cloud water droplets which are ad-vected in the flow and shrink or grow in correspondencewith the supersaturation at their position.

Bipin KumarTechnische Universitat [email protected]

196 DS13 Abstracts

Raymond [email protected]

Joerg SchumacherTechnische Universitat [email protected]

MS94

Revisiting the Scaling Analysis of Irreversible Ag-gregation Dynamics

The analysis of the size distribution of droplets condensingon a substrate is a test ground for scaling theories. Sur-prisingly, a faithful description of its evolution must ex-plicitly address microscopic nucleation and growth mecha-nisms of the droplets. In view of this we discuss here, howthis breaking of universality relates to other systems withvastly polydisperse droplet size distributions, as they willbe discussed in subsequent talks.

Jurgen VollmerMax Planck Institute for Dynamics and [email protected]

MS94

Understanding Rainfall: Collisional Versus Non-collisional Mechanisms for Droplet Growth

I shall discuss the possible mechanisms for the growth ofmicroscopic water droplets in clouds into rain drops. Col-lisional mechanisms are not effective in a critical range ofdroplet sizes. Two non-collisional routes for droplet growthwill be considered: these are Ostwald ripening, and a newtheory for growth due to fluctuations in supersaturationtermed ’convective ripening’. Both mechanisms can beilluminated by experiments. I shall discuss experimentsby Juergen Vollmer and co-workers on a ’test-tube’ modelfor rainfall in a convectively stable atmosphere, which arenicely explained by invoking Ostwald ripening.

Michael WilkinsonDept. of Applied Math.The Open University, Milton Keynes - [email protected]

MS95

Bifurcation Phenomena in a 2D Discontinuous Map

The physical situations that give rise to discontinuous mapsare discussed and their 2D normal forms are explored. Thecharacter of the normal form depends on the derivatives ofthe map functions with respect to the parameters. Earlierwork explored the bifurcations in this system under someassumptions. Here we report some results on the mostgeneral case of 2D discontinuous map.

Soumitro BanerjeeIndian Institute of Science education & Research,Kolkata, [email protected]

MS95

Multistability and Arithmetically Period-addingBifurcations in Piecewise Smooth Dynamical Sys-tems

Multistability, as characterized by the coexistence of multi-

ple attractors, is common in nonlinear dynamical systems.In such a case, starting the system from a different ini-tial condition can result in a completely different final orasymptotic state. The behavior thus has implications tofundamental issues such as repeatability in experimentalscience. Existing works on multistability in nonlinear dy-namics focus mostly on smooth systems. A typical sce-nario for multistability to arise is when a Hamiltonian sys-tem becomes weakly dissipative so that a large number ofKolmogorovArnoldMoser (KAM) islands become sinks, orstable periodic attractors. There has also been an interestin nonsmooth dynamical systems. For example, piecewisesmooth systems have been known to arise commonly inphysical and engineering contexts such as impact oscilla-tors and switching circuits. Previous works have shownthat nonsmooth dynamical systems can exhibit bifurca-tions that have no counterparts in smooth systems. Theaim of this paper is to explore general phenomena associ-ated with multistability in nonsmooth dynamical systems.We shall use a generic class of piecewise smooth maps thatare representative of nonsmooth dynamical systems. Byfocusing on the weakly dissipative regime near the Hamil-tonian limit, we find that multistability can arise as a re-sult of various saddle-node bifurcations. A striking phe-nomenon is that, as a parameter characterizing the amountof the dissipation is decreased, the periods of the stableperiodic attractors created at the sequence of saddle-nodebifurcations follow an arithmetic order. We call such bifur-cations arithmetically period-adding bifurcations. We pro-vide physical analyses, numerical computations, and math-ematical proofs to establish the occurrence of these bifurca-tions. Our work reveals that multistability can be commonin nonsmooth dynamical systems, and its characteristicscan be quite different from those in smooth dynamical sys-tems.

Younghae DoKyungpook National [email protected]

MS95

Codimension Two Border Collision Bifurcations inPiecewise Monotone Discontinuous Maps

We consider the bifurcation structures which originate fromthe intersection point of two border collision bifurcationcurves. The classification of possible structures can be doneby using the first return map in a suitable interval aroundthe discontinuity point. This first return map is continuousat the codimension-2 point and the possible bifurcationstructures depend on the shape of its branches (increasingor decreasing). Additionally, the connection to the Lorenz-like flows is emphasized.

Laura GardiniUniversity of UrbinoDepartment of Economics, Society and [email protected]

MS95

Bifurcation Structure in a Piecewise Smooth Mapwith Two Kink Points

We consider a family of one-dimensional piecewise smoothmaps with two kink points. The map comes from an eco-nomic application. The bifurcation structure of the param-eter space is studied. Using the skew tent map as a normalform for border collision bifurcations (BCB) we define thetypes of attractors which appear due the BCB of the fixed

DS13 Abstracts 197

point. Peculiarities of the bifurcation structure related tothe horizontal branch of the map are described.

Iryna SushkoNational Academy of Sciences of Ukraine, Kiev, Ukraineira [email protected]

MS96

Marine Bioinvasion in the Network of Global Ship-ping Connections

Transportation networks play a crucial role for the spreadof invasive species. Here, we combine the network of world-wide cargo ship movements with environmental conditionsand biogeography, to develop a model for marine bioinva-sion. We classify marine ecoregions according to their to-tal invasion risk and the diversity of their invasion sources.Our predictions agree with observations in the field andreveal that invasion risks are highest for intermediate geo-graphic distances. Our findings suggest that network-basedinvasion models facilitate the development of targeted mit-igation strategies.

Bernd BlasiusICBM, University of [email protected]

MS96

Successful Strategies for Competing Networks

We investigate competition between networks and how todesign optimal strategies for the connection between them.Specifically, we consider two networks interacting throughconnector links and competing for centrality. We show howeach network can improve the outcome of this competitiveinteraction by carefully selecting the type of connector linksor reorganizing its internal structure. We also introduce acompetition parameter, which quantifies which network istaking advantage of the other in real situations.

Javier BulduUniversidad Politecnica de Madrid, Spain &Universidad Rey Juan Carlos, Madrid, [email protected]

Jacobo AguirreCentro de Astrobiologa, CSIC-INTA, [email protected]

David PapoUniversidad Politecnica de Madrid, [email protected]

MS96

Extreme Vulnerability of Network of Networks

Network science focused on studying a single isolated net-work that does not interact with other networks. In reality,many real-networks interact and depend on each other. Iwill present an analytical framework for the cascading fail-ures, critical threshold and the giant component of a net-work of networks. Such systems have many novel featuresthat are not present in classical network theory. More-over, interdependent networks embedded in space are sig-nificantly more vulnerable compared to random networks.

Shlomo HavlinBar-Ilan University

[email protected]

MS96

Network of Networks and the Climate System

We introduce a novel graph-theoretical framework forstudying the interaction between subnetworks within a net-work of networks which allows us to quantify the structuralrole of single vertices or whole subnetworks concerning theinteraction of subnetworks on local, mesoscopic and globalscales. Applying this to climate data uncovers interest-ing features of the atmospheres vertical stratification, toidentify interrelations of Indian and East Asian SummerMonsoon or to detect paleo-climatic variability transitionsrelated to human evolution.


Jonathan Donges, Reik Donner, Norbert Marwan, KiraRehfeldPotsdam Institute for Climate Impact [email protected], [email protected],[email protected], [email protected]

MS96

Synchronization in Populations of Chemical Os-cillators: Quorum Sensing, Phase Clusters andChimeras

We have studied large, heterogeneous populations of dis-crete chemical oscillators ( 100,000) to characterize twodifferent types of density-dependent transitions to synchro-nized oscillatory behavior. For different chemical exchangerates between the oscillators and the surrounding solution,we find with increasing oscillator number density (1) thegradual Kuramoto synchronization or (2) the sudden quo-rum sensing switching on. We also describe the formationof phase clusters and chimera states and their relation toother synchronization states. M. R. Tinsley, S. Nkomo,and K. Showalter, Nature Physics 8, 662 (2012).

Kenneth ShowalterWest Virginia UniversityDepartment of [email protected]

MS97

Modeling the Response of Coastal Ecosystems toNutrient Loading, Climate Change, and ShellfishAquaculture

Aquatic simulation models have emerged in recent decadesas critical tools for the heuristic study of ecosystem struc-ture and function. These models are also increasingly be-ing used to inform management decisions on a variety ofissues, particularly the effects of nitrogen abatement onthe cultural eutrophication of estuaries. These two goals(research and management) often present contrasting re-quirements for model resolution, parameterization, and ac-curacy. The trend in both areas has been towards increas-ingly complex and highly resolved models. Limitations ofthese models, however, include their long run times, exten-sive time and resources required for model development,lack of user-friendliness, and large number of state vari-

198 DS13 Abstracts

ables and parameters which can be difficult to constrain,especially in systems without adequate data for verificationof both state concentrations and rate processes. A grow-ing body of literature is calling for development of sim-ple and intermediate-complexity models as alternatives tothese complex approaches, and new approaches are beingdeveloped for use in parallel with more complex models in amove towards ensemble predictions much like weather andhurricane forecasts. I will present results from a variety ofsimple and intermediate-complexity modeling approachesin U.S. East coast estuaries with a focus on predicting sys-tem response to changes in anthropogenic nutrient load-ing, ongoing climate change, expansion of shellfish aqua-culture, and shellfish restoration. In addition to generat-ing heuristic understanding, these models are being usedto develop management recommendations and restorationalternatives, and are being deployed online for direct useby managers, educators, and other stakeholders.

Mark BrushVirginia Institute of Marine [email protected]

MS97

Size- and Stage-structured Population Model toAssess the Growth-mediated Effect of Environmen-tal Conditions on Population Dynamics

Population abundance fluctuates over time. The fluctua-tion is caused by changes in survival and/or reproductiverates (vital rates). Determining how vital rates fluctuateand how they in turn affect population abundance is one ofthe main objectives of population biology. One of my cur-rent research focuses on investigating the effects of environ-mental conditions on population dynamics of white shrimpin the Gulf of Mexico. Previous studies have demonstratedthat environmental conditions in an estuary affect individ-ual growth of post-larval and marsh-stage juvenile shrimp.From a field experimental study, age-size relationship wasdetermined. In addition, shrimps were sampled in situ todetermine their size distribution. From these two data sets,size-specific instantaneous mortality of young shrimp wasestimated. Then, a size- and stage-structured populationmodel was used to assess the effects of variable individualgrowth rates on annual population growth rate. The resultshows that the finite annual population growth rate canrange from 0.4 to 1.1 based on the observed range of indi-vidual growth rate. Finally, the implication of the resulton transient and asymptotic yield is discussed.

Masami FujiwaraTexas A&M [email protected]

MS97

Nonlinear Effects in Size-structured Models of Zoo-plankton Communities

There exist many challenges, both biological and mod-eling, inherent in marine ecosystems. The talks in thismini-symposium cover a wide-range of topics, from shell-fish to phytoplankton. This introductory talk will intro-duce the topics that will be covered throughout this mini-symposium and some of the common modeling strategiesthat will be employed. Many of the overarching questionswill be discussed, such as the effect of nutrient availabilityand climate change on population dynamics. The final partof the talk will explore some of these themes in a specific

size-structured model of zooplankton communities.

M. Drew LaMarCollege of William and [email protected]

MS97

The Response of a Size-structured Plankton Com-munity to Environmental Variability

The influence of fluctuating environmental conditions onplankton community structure is investigated in an ideal-ized model for size-dependent phytoplankton-zooplanktoninteractions. When the model is forced with periodic nu-trient pulses, the phytoplankton total abundance and sizedistribution are both controlled by the allometric relation-ships describing growth and grazing and by the ampli-tude and frequency of pulses. Results are compared toobserved relationship between total chlorophyll and the rel-ative abundance of small/large phytoplankton cells.

Ariane VerdyScripps Institution of [email protected]

MS98

Time-delayed Switching Control of Structures withUncertainties

Models of balance with on-off control have attracted recentattention, in mechanics, robotics, and biology. We con-sider the influence of noise in these on-off systems throughcanonical models of balance, considering different noisesources in the setting of act-and-wait control, and con-trast with randomness in feedback (state-dependent) con-trol. Conditions for noise-sustained transients, typicallyundesirable in balance, are provided using numerical andanalytical approaches.

Rachel KuskeUniversity of British [email protected]

MS98

Oscillators with Large Delay

Differential equations with a large delay in one of theirarguments show features reminiscent of spatially extendedsystems. Eigenvalues of equilibria and periodic orbits tendto form bands, for which one can derive easily computableformulas. This permits us to draw conclusions for a systemwith given coefficients but increasing delay. For example,one can find criteria, which ensure the co-existence of largenumbers of stable periodic orbits for large delays.



Matthias WolfrumWIAS [email protected]

DS13 Abstracts 199

MS98

Dynamic Contact Problems Modeled by DelayedOscillators

Dynamic contact problems are in the forefront of mechan-ical engineering research due to the expensive laboratoryexperiments and high-performance computing used at in-dustrial R&D level. These multi-scale problems can suc-cessfully be transformed to delayed oscillators; this opensway to their analytical study needed for model validationand for testing numerical codes. Rolling of elastic wheelsand cutting of metals are discussed as relevant examplesleading to non-autonomous delay-differential equations likethe delayed Mathieu equation paradigm.

Gabor StepanDepartment of Applied MechanicsBudapest University of Technology and [email protected]

MS98

Irregular Motion Caused by State-dependent Delay

For π2< α < 5π

2the simple linear equation

x′(t) = −αx(t− 1) ∈ R

has only non-real characteristic values, 2 in the right half-plane and the others in the left halfplane. We construct astate-dependent delay

dU : C ⊃ U → (0, 2)

with dU (φ) = 1 for φ close to 0 ∈ C = C([−2, 0],R) insuch a way that the equation

x′(t) = −αx(t− dU (xt))

has a homoclinic solution x = h,

h(t) → 0 as |t| → ∞, 0 �= ht = h(t+·) ∈ C1 = C1([−2, 0],R).

The flowline

R t �→ ht ∈ X

= {φ ∈ U ∩ C1 : φ′(0) = −αφ(−dU(φ))}is a minimal intersection of the stable and unstable man-ifolds at equilibrium in the solution manifold X. Thisshould imply chaotic motion close to the homoclinic loop.

Hans-Otto WaltherUniversity of [email protected]

MS98

Delayed Control of Self-excited Vibrations in Elas-tic Structures

Flutter is an aeroelastic self-excited oscillation of aircraftwing with high frequency and large amplitude; it can causea loss of structural integrity in wings. As active control hasbecome a major method for flutter suppression of aircraftwings, it results in some new problems induced by the timedelay in the controllers and filters. Both the negative andpositive effects of the time delay on the flutter suppressionof aircraft wings are discussed in this talk, but the positiveeffect is emphasized.

Zaihua WangNanjing University of Aeronautics and Astronautics

[email protected]

MS99

Zonal Jets and Meridional Transport Barriers inPlanetary Atmospheres

Theoretical results relating to KAM theory have led tothe expectation that associated with zonal (west–east) jetstreams in planetary atmospheres should be barriers whichinhibit meridional (south–north) transport. Evidence willbe provided for this expectation based on the analysis of: 1)winds produced by an idealized model of Jupiter’s weatherlayer; and 2) winds produced by a comprehensive model ofthe Earth’s stratosphere. This will follow a review of therelevant KAM theory results.

Francisco J. Beron-VeraUniversity of [email protected]

MS99

Periodic Orbits and Transition to Chaos in Many-degrees-of-freedom, Mean-field Hamiltonian Sys-tems

A study of transition to chaos in many-degrees-of-freedomsystems is presented in the context of mean-field-coupledsymplectic maps. The coupling is motivated by weaklynonlinear descriptions of plasmas and fluids. We focus onreversible twist and nontwist systems, and use continuationmethods to compute symmetric periodic orbits with givenrotation vectors. Preliminary ideas are presented on ap-proximation of N-dimensional tori by periodic orbits, andthe transition to chaos due to the destruction of the tori.

Diego Del-Castillo-NegreteOak Ridge National [email protected]

Arturo OlveraIIMAS-UNAM, [email protected]

MS99

Singularity Theory for Non-twist KAM Tori: AMethodology

We present a novel methodology to find a classify non-twistKAM tori in degenerate Hamiltonian systems.The classifi-cation of KAM tori which is based on Singularity Theory.The results are presented in an a posteriori format that letus to deal with far from integrable Hamiltonian systems.Remarkably, the proofs lead to numerical algorithms forcomputing non-twist KAM tori. This talk aims to illustratethe main ideas of our approach, including some numericalexamples.

Alex HaroUniversitat de BarcelonaUniversitat de Barcelona Gran Via 58508007 Barcelona(Spain)[email protected]

Rafael de la LlaveGeorgia Institute of Technology, [email protected]

Alejandra Gonzalez-Enriquez

200 DS13 Abstracts

Universitat de [email protected]

MS99

Breakup of Invariant Tori of Volume PreservingMaps

KAM theory predicts that Diophantine, two-tori of 3Dvolume-preserving maps are robust. Though a torus withfixed rotation vector is fragile, robustness pertains to one-parameter families. We show that the breakup thresholdcan be predicted using an extension of Greene’s residuecriterion. Another of Greene’s conjectures is that noblecircles are locally most robust. We study the 3D analogueby investigating the robustness of tori with rotation vectorsfrom cubic fields.

James D. MeissUniversity of ColoradoDept of Applied [email protected]

Adam M. FoxUniversity of Colorado, [email protected]

MS99

Numerical Extension of the Center-stable andCenter-unstable Manifolds of the Collinear Libra-tion Points of the Spatial, Circular RestrictedThree-body Problem

Results will be presented on the computation of the familiesof 2-dimensional invariant tori around the collinear equi-librium points of the restricted three-body problem, thatspan most of the center manifolds of these points. The lin-ear approximation of their stable and unstable manifoldswill also be covered. The different families of tori involvedwill be extended up to their natural termination or thecomputational limit of the numerical methodology used,that will also be discussed.

Josep-Maria MondeloUniversitat Autonoma de [email protected]

Esther BarrabesUniversitat de [email protected]

Gerard GomezDepartament de Matematica AplicadaUniversitat de [email protected]

Merce OlleUniversitat Politecnica de [email protected]

MS100

Geometric Methods Applied to Non-holonomicMechanics

In this talk we discuss some of the geometry behind thetheory of nonholonomic systems. In particular we discusswhen measure is preserved in various systems and the na-ture of the ensuing dynamics. We also discuss analogies of

such systems with certain optical systems.

Anthony M. BlochUniversity of MichiganDepartment of [email protected]

MS100

Integrability and Quantization: A Geometric Ap-proach


Oscar FernandezIMA, University of [email protected]

MS100

Geometry of the Three Body Problem


Richard MontgomeryUniversity of California at Santa [email protected]

MS100

Geometric Mechanics of Elastic Rods in Contact

One of the most challenging and basic problems in elas-tic rod dynamics is a description of rods in contact thatprevents any unphysical self-intersections. Most previ-ous works addressed this issue through the introduction ofshort-range potentials. We study the dynamics of elasticrods with perfect rolling contact which is physically rele-vant for rods with rough surface. Such dynamics cannotbe described by the introduction of any kind of potential.We show that, surprisingly, the presence of rolling contactin rod dynamics leads to highly complex behavior even forevolution of small disturbances.

Vakhtang PutkaradzeColorado State [email protected]

MS101

Measure Solutions for Some Models in PopulationDynamics

We give a direct proof of well-posedness of solutions to gen-eral selection-mutation and structured population modelswith measures as initial data. This is motivated by the factthat some stationary states of these models are measuresand not L1 functions, so the measures are a more naturalspace to study their dynamics. Our techniques are based ondistances between measures appearing in optimal transportand common arguments involving Picard iterations. Thesetools provide a simplification of previous approaches andare applicable or adaptable to a wide variety of models inpopulation dynamics.

Jose A. CanizoDepartment of Pure Mathematics and MathematicalStatisticsUniversity of [email protected]

Jose Carrillo

DS13 Abstracts 201

Department of MathematicsImperial College [email protected]

Sılvia CuadradoDepartament de MatematiquesUniversitat Autnoma de [email protected]

MS101

Kinetic Models for Opinion Formation

We discuss nonlinear kinetic models for opinion formation.The evolution is described by systems of Boltzmann-likeequations. We show that at suitably large times, in pres-ence of a large number of interactions in each of whichindividuals change their opinions/positions only little, thenonlinear systems of Boltzmann-type equations are well-approximated by systems of Fokker-Planck type equations,which admit different, non-trivial steady states.

Bertram DuringUniversity of [email protected]

MS101

Flocking Dynamics and Mean-field Limit in theCucker-Smale-type Model with Topological Inter-actions

Motivated by recent observations of real biological systems,we introduce a Cucker-Smale-type model with interactionbetween agents depending on their topological distance,measured in units of agents’ separation. We study theconditions leading to asymptotic flocking, i.e., finding avelocity consensus. Moreover, introducing the concept oftopological distance in continuum descriptions, we showhow to pass to the mean-field limit, recovering kinetic andhydrodynamic descriptions.

Jan HaskovecRICAMAustrian Academy of [email protected]

MS101

Mathematical Modeling and Simulation of Pedes-trian Motion

We present different modeling approaches for the motion oflarge pedestrian crowds and their efficient numerical sim-ulation. We start on the microscopic level and discussthe transition to the corresponding meso- and macroscopicmodels. Here we focus on the particular interactions be-tween pedestrians and other specific modeling aspects, likemotion in congested areas. Pedestrian crowds show a com-plex dynamical behavior, which can be observed in themathematical models. These equations are in general non-linear and require flexible and efficient discretization tech-niques like discontinuous Galerkin methods. We illustratethis versatile behavior with numerical simulations.

Marie-Therese WolframDepartment of Mathematics, University of [email protected]

MS102

Mathematical and Statistical Modeling of HumanLymphocyte Proliferation with CFSE Data

Partial differential equation (PDE) models are presentedto describe lymphocyte dynamics in a CFSE proliferationassay. Previously poorly understood physical mechanismsaccounting for dye dilution by division, auto fluorescenceand label decay are included. The new models providequantitative techniques that are useful for the comparisonof CFSE proliferation assay data across different data setsand experimental conditions. Variability and uncertaintyin data and modeling are discussed.

H. T. BanksCRSC, NC State [email protected]

MS102

The Interaction of Antibiotic Drug Combinationsis Dynamic: the Genomic and Theoretical Basis ofRapid Synergy Loss in Edible E.coli

When antibiotic efficacy & multi-drug antibiotic interac-tions are measured in standard pharmacological proce-dures, their inhibitory effect is usually measured over oneday especially in academic studies. This is too short ifwe are to understand how drug efficacy changes over timebecause of evolution to treatment. The use of intensiveprocedures like ”colony counting” produce data based oncell yield at 24h & not on growth rate measures through-out the 24h period. So we evaluated drug interactions ona continuous basis, observing hundreds of generations inexperiments lasting days. Studies like this readily revealevolutionary dynamics and highlight the dynamically un-stable drug interactions. For example, the drug pair ery-thromycin & doxycycline kill synergistically over a ¡24-hourperiod & antagonise over longer periods. We show, usingmathematical models & whole-genome analyses that rapidgene duplication of several drug-resistance operons is re-sponsible for synergy loss.

Robert BeardmoreDepartment of MathematicsImperial College [email protected]

MS102

Ensemble Modeling of Immune Response to In-fluenza A Virus Infection

Human body responds to influenza infection by initiatinga spectrum of immune responses, ranging from innate toadaptive cellular and antibody, which are regulated by anintricate network of signaling interactions that have not yetbeen completely characterized. In the talk I will outline aseries of models that provide qualitative and quantitativeprediction of the time course of the disease, aid in under-standing of the mechanisms of the immune response, andhave been utilized in the study the effects of an antivi-ral drug treatment. Our latest effort has been focused onensemble models that reflect the uncertainty about param-eter values, data sparseness, and the likely variation of thedisease outcome across a population exposed to IAV. Thetechnique is useful when the model contains many unknownparameters, such as reaction rate constants of biochemicalprocesses, which are poorly constrained and their direct

202 DS13 Abstracts

measurement in vivo is not feasible.

David SwigonDepartment of MathematicsUniversity of [email protected]

MS102

Optimal Self-Sacrifice Facilitates Pathogen Inva-sion of the Gut

The interior lining of the human intestine is inhabited bypopulations of commensal microbiota, which provide de-fense against invasive bacteria. Surprisingly, SalmonellaTyphimurium gains an environmental advantage over thecommensals by provoking the hosts inflammatory defenses.Two hypotheses have been proposed to explain how S. Ty-phimurium gains this advantage: the food hypothesis anddifferential killing hypothesis. We develop and analyze amodel for how these effects interact to determine optimalstrategies for the Salmonella population.

Glenn S. YoungUniversity of PittsburghDepartment of [email protected]

MS103

Networks from the Bottom Up

Using a statistical physics exact formulation of transfer ofinformation from measurements to a model, we show howto complete Hodgkin-Huxley models of individual neuronsthrough estimation of fixed parameters and unobservedstates. The application of this to models of neurons inthe avian song system will be presented.

Henry D. AbarbanelPhysics DepratmentUniv of California, San [email protected]

MS103

Scale-invariant Brain Dynamics: Theory VersusExperiments

The idea that the brain as a dynamical system fluctuatesaround a critical point received compelling support whenneuronal avalanches were experimentally observed, theirdistributions of size and duration being compatible withpower laws [Beggs & Plenz, J. Neurosci. 23 11167 (2003)].Since then, other signatures of scale-invariant brain dy-namics were obtained in a variety of experimental setups.While models have been able to reproduce some of thesefeatures, many challenges remain and will be reviewed.

Mauro CopelliUniversidade Federal de PernambucoDepartment of [email protected]

MS103

How Synaptic Potentiation Balances Plasticity andStability Within An In Vitro Network of Neurons

Long-term potentiation (LTP) is widely believed to bethe physiological basis of learning and memory. Mecha-nisms underlying LTP have been studied extensively at the

monosynaptic level, but the effects of LTP on larger scalenetworks of neurons remain poorly understood. We chem-ically induce LTP in a cultured network of hippocampalneurons and show that after synaptic potentiation, a net-work of in vitro hippocampal neurons returns to a homeo-static state after widespread increases in firing.

Rhonda DzakpasuGeorgetown UniversityDepartment of [email protected]

MS103

Using Dynamical Information from One Node toEstimate the States and Parameters of Small Net-works of Coupled Neuronal Oscillators

We consider small dynamical networks of coupled oscilla-tors for which the network topology is unknown. Usingpartial knowledge of the oscillators’ dynamics we estimatethe coupling and state of each node. We focus on the casewhere the state time evolution from only one oscillator isavailable. We propose an adaptive strategy that uses syn-chronization between the true network and a replica net-work to estimate these features and apply it to small neu-ronal networks.

Francesco SorrentinoUniversity of New MexicoDepartment of Mechanical [email protected]

MS104

Stochastic Switching and Alternating ActivityBouts Resulting from Reciprocal Inhibition andApplications to Sleep-Wake Cycling

‘Sleep-active’ and ‘wake-active’ neurons in the brains ofmammals are thought to inhibit each other resulting bothin discrete states of sleep and wake and switching betweenthe two states. New behavioral data sheds light on the un-derlying neurophysiology. In infants, both sleep and wakebout durations have an exponential distribution with inde-pendent regulation of bout means. This suggests stochas-tic switching in a bistable system, and so we modeled thissystem as a pair of coupled, mutually inhibitory neuronsreceiving noisy driving currents. We examined bout du-rations of the two neurons, switching mechanisms, anddependence on system parameters. Regardless of param-eter choices, we found that bout durations of a neuronare always exponentially distributed. Furthermore, boutswitches were found to be primarily a consequence of re-lease from inhibition rather than escape via excitation, andwe found that inhibition allows independent control overbout lengths of the two neurons.

Badal JoshiDuke [email protected]

Mainak PatelDuke UniversityDepartment of [email protected]

MS104

Mutually Inhibiting Two Cluster Model for Sleep-

DS13 Abstracts 203

Wake Transitions

Sleep and wake states are governed by competitive inter-actions between neuronal networks, resulting in a powerlaw distribution of wake bout durations. We modeled twomutually-inhibiting random graphs where each neuron canbe in an excited, basal or inhibited state and fire accord-ing to a poisson process. Dynamics of the stochastic meanfield equations for population of each state neuron is inves-tigated to understand possible mechanisms of the powerlaw behavior of bout durations.

Jung Eun Kim, Janet BestThe Ohio State UniversityDepartment of [email protected], [email protected]

Fatih OlmezDepartment of MathematicsThe Ohio State [email protected]


John McsweeneyRose-Hulman Institute of [email protected]


MS104

Characterizing Bistability in Stochastic Processeson Modular Neural Networks

Many real-world networks, including neuronal networks,exhibit modularity: their nodes can be partitioned intosubsets with few links between, but many within. For astochastic process on a network with two mutually inhibit-ing modules, we expect to observe bistability – alternatingtime intervals where each cluster is highly activated. In thistalk we establish quantitative links between these vaguenotions of “bistability’ and “modularity’, as they relate tosleep-wake cycling dynamics.

John [email protected]

MS105

Experimental Study of Electrothermal 3D Mixingusing 3D MicroPIV

In lab-on-chips, micro-mixing is a keystep to perform fastand reproducible reactions. For the last thirty years, dy-namical system community has demonstrated that chaoticmixing must involve at least 3 dimensions. Yet, microflu-idic research community has scarcely studied 3D mix-ing. Meanwhile, electrokinetics has emerged as an elegantway to drive vortices. By overlapping vortices in 3 di-mensions, we present an original time dependent (3D+1)micro-mixer. Flows periodically stretch and fold, inducingchaotic advection, which is characterized by 3D μPIV.

Paul Kauffmann

University of California, Santa [email protected]

Sophie LoireUniversity of California Santa [email protected]

Igor [email protected]

MS105

Chaotic Fluid Mixing for AC Electrothermal Flowsby Blinking Vortices

We present an experimental and theoretical study of ACelectrothermal chaotic mixing using blinking of asymmet-ric 2D and 3D electrothermal vortices. Electrothermalflows are modelled by finite element method using COM-SOL software based on an enhanced electrothermal model.We use the mix-variance coefficient (MVC) and mix-normon experimental particle detection data and numerical tra-jectory simulations to evaluate mixing at different scalesincluding the layering of fluid interfaces by the flow, a key-point for efficient mixing. The blinking vortices methodgreatly improve mixing efficiency. The effect of blinkingfrequency and particle size is studied. Theoretical, experi-mental and simulation results of the mixing process will bepresented.

Sophie LoireUniversity of California Santa [email protected]

MS105

Creation and Manipulation of Lagrangian FlowStructures in 3D ACEO Micro-flows

Flow forcing by AC electro-osmosis (ACEO) is a promisingtechnique for the actuation of micro-flows. Its utilizationto date mainly concerns pumping and mixing. However,emerging micro-fluidic applications often demand multiplefunctionalities within one device. This is typically achievedvia complex system designs. The present study exploresfirst ways by which this may be accomplished in a standardmicro-channel via systematic creation and manipulation of3D Lagrangian flow structures using ACEO.

Michel SpeetjensLaboratory for Energy Technology, Dept. Mech. Eng.Eindhoven University of [email protected]

Hans de WispelaereEindhoven University of [email protected]

Anton van SteenhovenEindhoven University of [email protected]

MS105

Understanding Chaotic Mixing and Reversal UsingLinear Flow Models

It has long been known that convective diffusive irre-versibility in reversing Stokes flows can be used to sep-arate solutes based on diffusion. We consider a reversal

204 DS13 Abstracts

process in Stokes flows in the presence of weak diffusionusing chaotic and non-chaotic flows. We seek to under-stand the distinct effects that chaotic flows have on theloss of reversibility relative to non-chaotic flows using rate-independent observables. I will present results from numer-ical simulation for comparison of the two classes of Stokesflows. Using linear flows as models, I will show that thedecay of reversibility presents universal properties. In non-linear flows, I will show that this breaks down due to thedistribution of strain rates. In the limit of infinitesimal dif-fusivity, chaotic flows exhibit qualitatively distinct behav-ior with complete loss of sensitivity to the level of noise.Finally, I will discuss the relevance of the study of con-vective diffusive irreversibility in reversing flows to mixing.

Pavithra SundararajanCornell [email protected]

Joseph KirtlandAlfred [email protected]

Donald KochCornell UniversitySchool of Chemical and Biomolecular [email protected]

Abraham StroockCornell [email protected]

MS106

Elongated Swimming Particles in a Chaotic Ad-vecting Flow

We investigate the dynamics of self-propelled, point-like particles advected in a two-dimensional chaotic flow.Swimming is modeled as a combination of fixed intrinsicspeed and stochastic terms in translational and rotationalequations of motion. Interaction of active particles with thedynamical structures of flow leads to macroscopic effectson particle transport. We work with both spherical andellipsoidal swimmers and compare the two cases. We showthat elongated swimmers with high speed get attracted tothe unstable manifolds of hyperbolic fixed points; and theirtransport is enhanced relative to swimming spheres.

Nidhi KhuranaYale [email protected]

Nicholas T. OuelletteYale UniversityDepartment of Mechanical Engineering and [email protected]

MS106

Burning Manifolds in the Wake of a Cylinder

Passive chaotic advection in open flows, like in the flowaround a cylindrical obstacle, is governed by an invariantchaotic set. The long-time trajectories cover the unsta-ble manifold of the chaotic set, while its stable manifoldseparates the trajectories of different long-time behaviour.When an active process associated with front propagation

takes place in such flows, a possible approach to model thefront motion concerns the particles on the front as fluid el-ements having an orientation besides their position. Theirmotion can then be investigated as a low order dynami-cal system, in the spirit of burning manifolds that serve astransport barriers in such “chemical flows”. Now we aimat investigating the behaviour of this extended dynamicalsystem, taking the orientation of the front as an indepen-dent variable. We expect to gather information on howthe location of the burning manifold depends on the initialfront angle and velocity.

Gyorgy KarolyiBudapest University of Technology and [email protected]


MS106

Front Propagation in Fluid Flows: A Swimmer’sPerspective

This talk considers the generalization of passive advectivetransport to “active” media, specifically to media that sup-port some kind of front propagation: for example, the ex-pansion of chemical reaction fronts in microfluidic mixersor plankton blooms in large-scale oceanic flows. A low-dimensional nonlinear dynamics model, in which the frontelement can be viewed as a “swimmer” in the flow, is usedto predict the existence–and to explain the properties–of robust, one-sided barriers to front propagation. Wecall these barriers burning invariant manifolds (BIMs).BIMs play a central role in guiding the propagating frontsthrough the medium, determining the patterns formed bythe fronts, and in determining the average propagationspeeds. We compare our theory to table-top experimentsin magneto-hydrodynamically driven flows, and we high-light the role of BIMs for experimental phenomena, suchas the mode-locking and pinning of reaction fronts.

Kevin A. MitchellUniv of California, MercedSchool of Natural [email protected]

John R. MahoneyUniversity of California, [email protected]

MS106

Navigating the Lagrangian Flow Map – GloballyOptimal Feedback Control of Underpowered Vehi-cles in Time-varying Flow Fields

The optimal feedback control problem of interest takes theform of a time-varying HJB PDE. The solution of this PDE– the “value function’ – is the optimal cost-to-go as a func-tion of space and time. In the simplest case, the vehiclespeed is fixed, the value function depends solely on theposition of the vehicle at the fixed final time (making itconstant along optimal trajectories), and the optimal con-trol is simply to steer down the gradient of the value func-tion. Solving for the value function is difficult because it isneither C1 nor C0, due to the presence of locally optimaltrajectories and the small vehicle speed, respectively. Nev-ertheless, we compute the value function backwards in time

DS13 Abstracts 205

using a Godunov, semi-Lagrangian finite difference scheme.Moreover, we explain the relationship between the optimalcontrol and the Lagrangian structure of the flow itself, ob-serving the flow’s mapping of optimal trajectories from 3Dspace-time to the 2D time slice of interest.

Blane RhoadsUniversity of California Santa [email protected]


Andrew PojeMathematicsCUNY-Staten [email protected]

MS107

Time Delay and Symmetries in Antigenic Networks

In the studies of host-pathogen interactions, an importantrole is played by the structure of antigenic variants associ-ated with a pathogen, as well as the properties of immuneresponse. Using a model of antigenic variation in malaria,we illustrate how the methods of equivariant bifurcationtheory can be used to analyse symmetry properties of anti-genic networks and draw insightful conclusions about pos-sible dynamical behaviours. Particular attention is paid tothe role played by immune delay.

Konstantin BlyussUniversity of [email protected]

MS107

Time Delays and Clustering in Neural Networks

We study the existence and stability of cluster states ina network of inherently oscillatory neurons with time de-layed, all-to-all coupling. Cluster states are periodic solu-tions where the network splits into groups. Neurons withina group are synchronized, while neurons in different groupsare phase-locked with a fixed phase difference. We reducethe system of delay differential equations to a phase modelwhere the time delay enters as a phase shift and use thisphase model to show how the time delay affects the stabil-ity of various symmetric cluster states. Analytical resultsare compared with numerical bifurcation studies of the fullsystem of delay differential equations.

Sue Ann CampbellUniversity of WaterlooDept of Applied [email protected]

Ilya KobelevskiyImaging ResearchSunnybrook Health Sciences Centreilya [email protected]

MS107

Designing Connected Vehicle Systems with TimeDelays

Arising wireless communication technologies allow us es-tablish interactions between distant vehicles. Incorporat-

ing such information in nonlinear vehicle controllers mayextinguish nonlinear congestion waves triggered by humandrivers. On the other hand, these connections usually in-clude long delays which makes the design very challenging.In this talk we investigate the dynamics of connected ve-hicle systems at the linear and nonlinear level and lay outan experimental setup that allows one to test the designedalgorithms.

Gabor OroszUniversity of Michigan, Ann ArborDepartment of Mechanical [email protected]

MS107

Spatio-temporal Patterns in Lattices of Delay-coupled Systems

In our recent publications [Phys. Rev. Lett. 107 (2011)228102, Chaos 21 (2011) 047511] we show how spatio-temporal spiking patterns can be created in a ring of unidi-rectionally delay-coupled neurons. This talk reports abouta higher-dimensional extension of this technique. In partic-ular, arbitrary stable two-dimensional patterns can be cre-ated by a lattice of unidirectionally coupled neurons withperiodic boundary conditions (torus) with appropriatelyadjusted time delays.


MS108

Synchronizing Frequency Selective Maps

In cognitive radio, it is frequently desirable to avoid inter-fering with other transmitters by removing certain frequen-cies from a signal to be transmitted. I show here that it ispossible to design chaotic maps in which certain frequenciesare absent, and that these maps may be self-synchronized.The synchronized maps are resistant to interference withinthe excluded frequency bands.

Thomas L. CarrollNaval Reseach [email protected]

MS108

Chaotic Signals for Digital Communications

In this paper we present a system-level overview of theChaos modem prototype that we have developed. OurChaos modulation provides a BER lower than an uncodedBPSK and at the same time a bandwidth efficiency equalto that of BPSK with equivalent spreading. ImprovedLPI/LPD and AJ characteristics are also provided by ourChaos packets. Results on a communications video link de-veloped on our FPGA Chaos hardware platform with A/Dand D/A converters will be presented.

Roger Kuroda, Soumya Nag, Ning Kong, John EldonDatron World Communications, Inc.Datron Advanced Technology [email protected], [email protected], [email protected],[email protected]

206 DS13 Abstracts

MS108

Harnessing Chaos for Digital Communications

Chaotic signals have offered promise for secure communica-tions for more than two decades, yet have faced challengesin terms of synchronization, computational precision, andmodulation efficiency. Recent work at the Harris Corpo-ration has harnessed the core chaotic processes via ’digitalchaos’ in both FPGA and DSP implementations to effi-ciently achieve the desired goals of secure chaotic commu-nication systems within the bounds of practical software-defined hardware platforms.

Alan MichaelsHarris Corp.Government Communications Systems [email protected]

MS108

On the BER Performance of a Class of ChaoticSpreading Functions

This paper aims to analyze the performance of a particularclass of chaotic digital communication systems that uses aslice of a discrete-time chaotic function as the spreadingsequence. Using the cubic map as the spreading function ofchoice, this paper investigates the temporal and statisticalproperties of the cubic map, and then derives an expressionfor the bit error rate probability for this class of systems.A similar analysis is performed for a digital communicationsystem that uses a psuedorandom binary sequence as thespreading code. A comparision between the two systemsshows that the latter possesses a lower probability of biterror at the expense of being easier to detect as comparedto the chaotic digital communication system.

Ashitosh SwarupAshRem [email protected]

MS109

Data Assimilation for Two Model Problems: Tar-geted Observations and Parameter Estimation

We explore novel data assimilation (DA) techniques fortwo model problems, one forecasting the propagation of afront and the other a toy chaotic system. Using the localensemble transform Kalman filter (LETKF) DA method,we demonstrate LETKF with targeted observations basedon largest ensemble variance is skillful in outperformingLETKF with randomly located observations. We also ap-ply the hybrid ensemble Kalman filter parameter estima-tion method LETKF+sEnKF to further improve state es-timation skill.

Thomas BellskyArizona State [email protected]

Eric J. KostelichArizona State UniversitySchool of Mathematical & Statistical [email protected]

Alex Mahalovdepartement of mathematics,Arizona State [email protected]

MS109

Lagrangian Data Assimilation for Point-VortexSystems

Assimilating Lagrangian data (e.g. those from oceandrifters) into point-vortex models to estimate the unob-served vortex centres is a challenging filtering problem dueto nonlinear features of Lagrangian drifters that can failthe standard Kalman filter and its variants. Therefore,we adopt the particle filtering approach to assimilate in-formation from different launching positions of tracers forvarious point vortex systems. The results will gain ourunderstanding to the optimal launching positions to pre-dict/track large-scale eddies.

Naratip SantitissadeekornNorth Carolina Chapel [email protected]

MS109

A Hybrid Ensemble Kalman/Particle Filter for La-grangian Data Assimilation

Lagrangian data assimilation involves using observations ofthe positions of passive drifters in a flow in order to obtaina probability distribution on the underlying Eulerian flowfield. Several data assimilation schemes have been studiedin the context of geophysical fluid flows, but many of thesehave disadvantages. In this talk I will give an overviewof Lagrangian data assimilation and present results froma new hybrid filter scheme applied to the shallow waterequations.

Laura Slivinski, Bjorn SandstedeBrown Universitylaura [email protected], bjorn [email protected]

Elaine SpillerMarquette [email protected]

MS109

Estimating Parameters in Stochastic Systems: AVariational Bayesian Approach

Data assimilation can often be seen from a Bayesian per-spective, however most operational implementations intro-duce approximations based on a very small number of sam-ples (ensemble Kalman filter) to perform a statistical lin-earization of the system model, or seek an approximatemode of the posterior distribution (4DVAR). In statistics,alternative approaches are based on Monte Carlo samplingusing particle filters or path sampling, neither of which islikely to scale well enough to be applied to realistic modelsin the near future. This work introduces a new approach todata assimilation based on a variational treatment of theposterior distribution over paths.

Michail D. VrettasAston [email protected]

MS110

The Influence of Local Interactions Between Plantsand their Natural Enemies on Plant Diversity

Seedling patterns resulting from plant mortality due toseed predators and pathogens are hypothesized to play a

DS13 Abstracts 207

key role in maintaining plant diversity, while limited seeddispersal may contribute to species coexistence. I investi-gate how different patterns of dispersal and plant mortalityaffect seedling spatial patterns, and how these patterns re-late to plant coexistence using spatially explicit stochasticmodels that incorporate the multiple spatial and temporalscales over which these processes occur.

Noelle G. BeckmanThe Ohio State [email protected]

MS110

Stochastic Automaton Model for Ant Foraging andTerritorial Competition

We simulate cellular automaton with a set of individual-based rules to reproduce spatiotemporal dynamics arisingfrom local interactions of ants in colony. Ants deposit dif-fusible chemical pheromone that modifies local environ-ment for succeeding passages. Individual ants, then, re-spond to conspecific/heterospecific pheromone gradients,for example, by altering their direction of motion, orswitching tasks. We describe ant’s movement by rein-forced random walk, and use game-theoretic framework formodeling territorial conflicts. We study patterns (foragingtrails, territoriality, etc.) emerging from ‘microscopic’ in-teractions of individual ants. We derive macroscopic PDEsby considering continuum limits of the mechanistic micro-scopic dynamics, and compare the two models.

Arjun Beri, Arjun BeriMathematical Biosciences InstituteThe Ohio State [email protected], [email protected]

Debashish ChowdhuryDepartment of PhysicsIndian Institute of Technology, Kanpur, [email protected]

Harsh JainMathematical Biosciences InstituteThe Ohio State [email protected]

MS110

Trail Formation Based on Directed Pheromone De-position

Ants are able to build trail networks on a very large scale.The trails are based on the deposition of small amount ofchemicals called pheromones. In this talk, we introducean Individual-Based Model to describe the formation ofthese networks. The novelty of the model is to considerdeposited pheromones as small pieces of trails that each antcan follow. Numerically, we observe the emergence of largeand flexible networks. We analyze how the trail patternsdepend on the strength of the ant-pheromones interactionand show the existence of a phase transition. Finally, weintroduce the kinetic and macroscopic limit of the model.

Sebastien MotschCSCAMM, University of [email protected]

MS110

Derivation of Coarse-Grained Models of Bi-

Directional Pedestrian Traffic From Stochastic Mi-croscopic Dynamics

Microscopic rules for pedestrian traffic in a narrow streetor corridor are discussed and the corresponding stochas-tic system modeling the pedestrian bi-directional flow isintroduced. Mesoscopic and macroscopic PDE models forthe pedestrian density are derived. The macroscopic PDEmodel is a system of conservation laws which can changetype depending on the strength of interaction between thepedestrian flows and initial conditions. Behavior of thestochastic and the coarse-grained models is compared nu-merically for several different regimes and initial condi-tions. Finally, nonlinear diffusive corrections to the PDEmodel are derived systematically. Numerical simulationsshow that the diffusive terms can play a crucial role whenthe conservative coarse-grain PDE model becomes non-hyperbolic.

Ilya TimofeyevDept. of MathematicsUniv. of [email protected]

Alina ChertockNorth Carolina State UniversityDepartment of [email protected]

Alexander KurganovTulane UniversityDepartment of [email protected]

Anthony [email protected]

MS111

The Wiggling Trajectories of Bacteria

Many motile bacteria display wiggling trajectories, whichcorrespond to helical swimming paths. We observe andquantify the helical wiggling trajectories of Bacillus sub-tilis and show that flagellar bundles with fixed orientationrelative to the cell body are unlikely to produce wigglingtrajectories with pitch larger than 4 μm. On the otherhand, multiple rigid bundles with fixed orientation, simi-lar to those recently observed experimentally, are able toproduce wiggling trajectories with large pitches.

Henry FuUniversity of Nevada, RenoDept. Mechanical [email protected]

MS111

Cellular Dynamics Involved in Immune ReactionsDuring Healing Processes

We propose a partial differential equation model adaptedfrom the principles of wound healing studies and ana-lyze it to gain insights regarding the dynamics of immunecells/proteins following the insertion of a foreign body.Specifically we look at the multiple roles of macrophagesand the conditions for stabilizing/destabilizing the equi-librium state. Furthermore, we investigate the impact ofmesenchymal stem cells on the stability and the transient

208 DS13 Abstracts

behavior of the system.

Larrissa OwensUniversity of Texas at [email protected]

Jianzhong SuUniversity of Texas at ArlingtonDepartment of [email protected]

Akif IbaguimovTexas Tech [email protected]

MS111

Pairwise Interaction in Micro-swimming

A key observation in experiments and numerical simula-tions of suspensions of micro-swimmers is that ’pushing’organisms have a stronger tendency toward alignment com-pared to ’pulling’ organisms. It is impossible to character-ize the above phenomena without making reference to two-point statistics of the system such as orintational correla-tions of pairs of swimmers. It is therefore natural to seek anunderstanding of the behavior of an isolated pair of swim-mers as a first step to understanding these systems. Suchan analysis leads to a two way diffusion problem. Properboundary conditions as well as approximate solution meth-ods for this problem will be discussed. Subsequently thepairwise solution will be used to try to characterize thebehavior of a multi-body suspension.

Kajetan Sikorski, Peter R. KramerRensselaer Polytechnic InstituteDepartment of Mathematical [email protected], [email protected]

Patrick UnderhillRensselaer Polytechnic InstituteDepartment of Chemical and Biological [email protected]

MS111

Multiscale and Hybrid Models of Bacterial Chemo-taxis

Chemotaxis is the directed cell movement in response toexternal chemical signals. Bacterial chemotaxis is a criti-cal process in bacterial infections and bioremediation. Atthe population level, bacterial chemotaxis has been mod-elled by macroscopic Patlak-Keller-Segel equations. How-ever, these equations do not match recent experimentaldata in oscillatory signal fields. In this talk, I will presentour recent progress in deriving PDE models of bacterialchemotaxis from descriptions of single-cell signalling andmovement, and comparisons of PDE models with hybridmodels that integrate more details of single cell signalingand movement. Through these results I will clarify the per-formance and applicability of PKS equations in modellingbacterial chemotaxis.

Chuan XueOhio State [email protected]

MS112

A Time Since Last Infection-Dependent Epidemio-

logical Model

The aim of this work is to propose a model for infectiousagents with transmission rates that vary during the in-fectious period, and/or that can cause reinfection. Ex-istence, positivity, regularity, continuity of the solutions,and analysis of the existence and stability of equilibria isconducted using strongly continuous nonlinear semigroups.The model exhibits interesting outcomes, including exis-tence of multiple endemic equilibria, backward bifurca-tions, and endemic equilibria even in the absence of vitaldynamics.

Jorge Alfaro-MurilloDepartment of MathematicsPurdue [email protected]

MS112

Resistance to Larvicides in Mosquito Populationsand How It Could Benefit Malaria Control

Wemodel larviciding of mosquitoes taking into account theevolution of resistance to the larvicides, the evolutionarycosts of resistance and the implications for malaria control.A possible malaria control strategy is to shorten this adultlifespan by larviciding with a potent larvicide to whichmosquitoes become resistant. This novel strategy is stud-ied using a mathematical model for the wild type and resis-tant mutants and by incorporating the malaria disease dy-namics using an SEI type model with standard incidencethat incorporates the latency period of the parasite in wildtype and resistant mosquitoes.

Rongsong LiuDepartments of Mathematics and Department of ZoologyUniversity of [email protected]

MS112

Mathematical Modeling of the HIV/AIDS Epi-demic in Cuba

HIV is a pandemic which has accounted for more than 30million deaths since 1981. The Caribbean nation of Cuba,where HIV/AIDS prevalence is reported to be less than0.1%, has remained remarkably unscathed. The success inCuba can be attributed to its extremely effective nationalprogram for the prevention and control of HIV/AIDS, ini-tiated in 1983. In this talk, I will discuss the strategies thatthe Cuban government has taken to monitor and managethe HIV/AIDS epidemic. I will present a detailed qual-itative analysis of the governing nonlinear system of dif-ferential equations and then provide a more general modelthat divides the undiagnosed HIV-infected class into twoclasses, one containing individuals who acquired the in-fection via sexual transmission, and the other containingindividuals who acquired the infection via nonsexual trans-mission, which can serve as a model for other regions ofthe world in which transmission by nonsexual means playsa substantial role.

Antonio MastroberardinoDepartment of MathematicsThe Behrend [email protected]

MS112

Endemic Bubbles Generated by Delayed Behav-

DS13 Abstracts 209

ioral Response in Epidemic Models

Several models have been proposed to capture the phe-nomenon that individuals modify their behavior during anepidemic outbreak. This can be due to directly experi-encing the rising number of infections, media coverage, orintervention policies. In this talk we show that a delayedactivation of such a response can lead to some interestingdynamics. In the case of SIS type process, if the response isnot too sharp, the system preserves global stability. How-ever, for sharp delayed response, we can observe stabilityswitches as the basic reproduction number is increasing.First, the stability is passed from the disease free equilib-rium to an endemic equilibrium via transcritical bifurcationas usual, but a further increase of the reproduction num-ber causes oscillations, which later disappear, forming astructure in the bifurcation diagram what we call endemicbubble.

Gergely RostBolyai Institute, University of SzegedSzeged, Aradi vertank tere 1, H-6720 [email protected]

MS113

Computing Optimal Paths in Stochastic DynamicalSystems with Delay

Based on variational theory, we present a numericalmethod for computing optimal transition pathways instochastic differential equations with delay. We computethe most probable transition path (represented as hetero-clinic structures) resulting from the iterative solution ofa two-point boundary value problem which minimizes theaction in a corresponding deterministic Hamiltonian sys-tem. We apply it to continuous stochastic systems, suchas noisy nonlinear oscillators, and large discrete systems,such as epidemic rare events.

Brandon S. LindleyNaval Research [email protected]

MS113

Interplay of Bistability, Noise, and Time-delay inSemiconductor Lasers: Complex Dynamics and Po-tential Applications

I present experimental, numerical, and analytical resultson noise induced square-wave (SW) switching in lasers withtime-delayed feedback/coupling. The SWs are optically in-duced and controlled by the delay, making them attractivefor applications. Stable SWs occur for adequate param-eter regions; outside these regions the SWs are transienttowards the model steady-states. Due to delay-noise inter-actions, we show that noise can be exploited to increasethe duration of the SW transient.

Cristina MasollerUniversitat Politecnica de Catalunya (UPCDepartament de Fsica i Enginyeria Nuclear (DFEN)[email protected]

MS113

Synchronization of Degrade and Fire Oscillators bya Common Diffusible Activator

Delayed feedback has successfully been used to describe avariety of biological oscillators, both natural and synthetic.

A recent example is the application of a delayed negativefeedback formalism (degrade and fire) to model a popula-tion of oscillators that are synchronized by a diffusible ac-tivating signal. We present analytical and computationalresults for the synchronization of an ensemble of degradeand fire oscillators which couple through a common delayedpositive feedback signal.

William H. MatherVirginia [email protected]

Jeff HastyDepartment of BioengineeringUniversity of California, San [email protected]

Lev S. TsimringUniversity of California, San [email protected]

MS113

Statistical Multi-moment Bifurcations in RandomDelay Coupled Swarms

We study randomly distributed time delay coupling on thedynamics of large systems of self-propelling particles. Bi-furcation analysis reveals patterns with certain universalcharacteristics that depend on distinguished moments ofthe time delay distribution. We numerically and analyti-cally show that complex bifurcating patterns depend on allof the moments of the delay distribution. Moreover, thereis a noise intensity threshold that forces a transition of theswarm from a misaligned state into an aligned state.

Luis Mier-y-TeranJohns Hopkins Bloomberg School of Public [email protected]

Brandon S. LindleyNaval Research [email protected]


MS114

Leading from Within: New Leadership Models inSwarms

We report on efforts to analyze models of swarms withcovert leaders. In three-zone swarming, individual behav-ior is driven by the position and orientation of neighboringindividuals in each of three concentric zones, correspondingto repulsion, orientation and attraction respectively. Thefundamental purpose of this research is to understand howleadership affects the underlying dynamics and informa-tion transfer within the swarm, and we discuss new sta-bility boundaries for continuum models for swarming withleadership.

Louis F. RossiUniversity of [email protected]

210 DS13 Abstracts

MS114

A Nonlocal Continuum Model for Locust PhaseChange and Swarming

The desert locust Schistocerca gregaria has two intercon-vertible phases, solitarious and gregarious. Solitarious(gregarious) individuals are repelled from (attracted to)others, and crowding biases change towards the gregari-ous phase. We construct a model of the interplay betweenphase change and spatial dynamics leading to locust ag-gregations. The model is a system of nonlinear, nonlocaladvection-reaction equations. We derive instability con-ditions for the onset of a locust aggregation, character-ized by collective transition to the gregarious phase. Viaa model reduction to ODEs describing the bulk dynamicsof the two phases, we calculate the proportion of the pop-ulation that will gregarize. Numerical simulations revealtransiently traveling clumps of insects and hysteresis.

Chad M. TopazMacalester [email protected]

Maria D’[email protected]

Leah Edelstein-KeshetUniversity of British ColumbiaDepartment of [email protected]

Andrew J. BernoffHarvey Mudd CollegeDepartment of [email protected]

MS114

Social Intelligence: How Grouping Leads to Effec-tive Information Use in Mobile Animals

In this talk I will present some recent work on informa-tion and its use within swarming systems. I will outlinesome empirical results pertaining to information sharingin schooling fish. I will then present some reduced modelsbased around simple coordination games, that capture thesame qualitative features as the real systems, such as local-ized interaction, social influence, and rapid transitions toordered states, but which allow some analytical treatment.

Colin TorneyPrinceton [email protected]

MS114

Design and Prediction of Co-dimension One Pat-tern Formation of Non-local Collective Motion

In this talk we present recent results on pattern forma-tion of objects modeled by particles which obey non-localcollective motion laws. More specifically, we develop a non-local linear stability analysis for particles which aggregateuniformly on a d−1 sphere. Remarkably, linear theory ac-curately characterizes patterns in the ground states fromthe instabilities in the pairwise potential. This aspect ofthe theory allows us to design specified potentials whichassemble into targeted patterns.

David T. Uminsky

University of San FranciscoDepartment of [email protected]

MS115

Efficient Computation of Invariant Tori in VolumePreserving Maps

Volume preserving maps naturally arise in the study ofincompressible fluid flows. Codimension one invariant toriplay a fundamental role in the dynamics of these maps asthey form boundaries to transport within the system. Inthis talk I will present a quasi-Newton scheme to computethe invariant tori of three-dimensional, volume-preservingmaps. I will further show how this method can be used topredict the perturbation threshold for their destruction.

Adam M. FoxUniversity of Colorado, [email protected]

James D. MeissUniversity of ColoradoDept of Applied [email protected]

MS115

Transport in a 3D + 1 Ocean

A central theoretical difficulty in ring dynamics is thelack of unambiguous phenomenological criteria for quan-tifying their formation. We study the separation of EddyFranklin, formed during the DeepWater Horizon incident,with the data assimilating Naval Research LaboratoryRELO model. A strong hyperbolic region with intersectingstable and unstable 2D material surfaces marked ring sep-aration. The hyperbolicity developed simultaneously at alllevels. Intersecting stable and unstable manifolds providesan easily diagnosed signal of ring separation.

Denny KirwanUniversity of [email protected]

Pat HoganNaval Research Laboratory, Stennis Space Center, [email protected]

Helga S. HuntleyUniversity of [email protected]

Gregg [email protected]

Bruce Lipphardt, Mohamed SulmanSMSP, University of Delaware, Newark DE [email protected], [email protected]

MS115

Finite-Time Transport in Aperiodic Volume-Preserving Flows

We present a new method for computing the volumes oflobes comprising finite-time transport between arbitrarily-

DS13 Abstracts 211

defined regions in aperiodic volume-preserving flows. Com-pared to a standard volume integral approach, our methodprovides a reduction in dimension of the trajectory infor-mation necessary to compute these lobe volumes. We in-troduce the theory in 2D, and illustrate its application bycomputing transport within a simple model of a 3D aperi-odic rotating Hills vortex.

Brock MosovskyDepartment of Applied MathematicsUniversity of Colorado, [email protected]

MS115

Dynamical Systems Analysis of a Three-dimensional Time-dependent Ekman-driven FluidFlow

Techniques from the dynamical systems theory are appliedto study a 3-dimensional time-dependent fluid flow in a ro-tating cylinder. The circulation in this system is drivenby a stress imposed at the upper surface. The motionin a radially symmetric steady background state is regu-lar (non-chaotic), whereas the perturbed asymmetric time-dependent flow is characterized by the presence of bothregular and chaotic fluid parcel trajectories, with regularregions acting as transport barriers. This is consistent withan extension of the KAM theorem. Chaotic motion arisesas a result of resonances, and a formula for the resonancewidths is derived. A simple kinematic model is used tostudy the geometry of barriers, manifolds, resonances, andother objects that provide a template for chaotic stirringin this flow. A high-resolution spectral element model isthen used to check the validity of our results in realisticsettings and to explore different parameter regimes.

Irina Rypina, Lawrence PrattWoods Hole Oceanographic [email protected], [email protected]


MS116

Observability-based Sensor Placement for Biologi-cal and Bio-inspired Systems

The focus of the work in this project is the exploration ofthe coupling of control and sensing in nonlinear dynamicalsystems. These methods are being developed with a focuson tracking of position and strength of vortices behind apitching and heaving airfoil, strain sensor distribution indeformable insect wings for agile flight, and relative loca-tions of sensors and actuators in engineered and biologicalsystems.

Kristi Morgansen, Brian HinsonDept. of Aeronautics and AstronauticsU. of [email protected],[email protected]

MS116

Designing Dynamics for Cooperative Learning byMultiple Agents

We consider the problem of designing distributed dynam-

ics capable of learning an unknown vector from intermit-tent, noisy measurements made by multiple agents subjectto time-varying communication restrictions. We proposea simple individual agent dynamic and study performanceof the interconnected system. Our main results bound thelearning speed of these dynamics in terms of combinato-rial measures of the time-varying graph sequence, whichencodes the restricted communication among the agents.

Naomi E. LeonardPrinceton [email protected]

Alexander OlshevskyUniversity of Illinois at [email protected]

MS116

Distributed Control and Optimization for Spa-tiotemporal Sampling

This talk will present two approaches for optimization ofspatiotemporal sampling with multiple vehicles. First, co-ordinated trajectories for sampling a parametrized flowfieldare optimized using the empirical observability gramianfrom nonlinear observability. Second, sampling trajecto-ries are designed for nonstationary fields in which the spa-tial and temporal statistics may vary in space and time.In both approaches, we use tools from nonlinear control,specifically Lyapunov-based control, to design decentral-ized algorithms for stabilization of multi-vehicle samplingformations.

Derek A. Paley, Levi DeVries, Nitin SydneyUniversity of MarylandDepartment of Aerospace [email protected], [email protected],[email protected]

MS116

Distributed Control of Mobile Sensing ResourceDistribution in Flows

We consider distributed control policies to enable a team ofhomogeneous agents to maintain a desired spatial distribu-tion in a geophysical flow environment. Stability propertiesof the ensemble dynamics of the distributed control poli-cies are presented in the presence of uncertainty. Sincerealistic quasi-geostrophic ocean models exhibit double-gyre flow solutions, we use a wind-driven multi-gyre flowmodel to verify the proposed distributed control strategyand compare our control strategy with a baseline deter-ministic strategy.


Ani Hsieh, Ken MalloryDrexel [email protected], [email protected]

MS117

Symmetries and Compositionality for Control inComplex Cyber-Physical Systems

This talk considers control of symmetric systems, which

212 DS13 Abstracts

are systems, typically cyber-physical systems, which arecomprised of many diffeomorphically-related componentsthat are interconnected in a regular manner. Specifically,we consider a set of generators, X, and an associated group,G. Two components are interconnected if g1 = sg2 withs ∈ X and g1, g2 ∈ G. Two different systems, G1 and G2,are defined as equivalent if they have the same generatorsand identical component dynamics (they will be differentif they have different relations).

Bill GoodwineUniversity of Notre DameDepartment of Aerospace & Mechanical [email protected]

MS117

Incorporating Uncertainties in Dynamics and Ob-servations for the Prediction Problems in Geophys-ical Systems


Kayo IdeDept. of Atmospheric and Oceanic SciencesUniversity of Maryland, College [email protected]

MS117

Mixing with Natural Convection

The mixing properties of a natural convective flow insidea cubic box with time-dependent temperatures on the ver-tical walls are explored. We identify the symmetry planes,periodic lines and invariant surfaces for the correspondingStokes problem following the methodology of Clercx andcolleagues. Using Poincar maps, elliptic and hyperbolicsegments of the periodic lines are found. The topologi-cal changes introduced on the invariant surfaces due to anonlinear perturbation, are briefly discussed.

Luis M. de la Cruz, Nicolas RodriguezGeophysics [email protected], nick [email protected]

Sebastian Contreras, Eduardo RamosCenter for Energy [email protected], [email protected]

MS117

Nonlinear Effects of Electrostatics in IndustrialProcesses

Electrical charging of agitated grains is an archetypal ex-ample of a many-body system far from equilibrium that ex-hibits highly organized - and enormously powerful - collec-tive behaviors such as multi-million volt lightning in sand-storms. In this talk, we present a simple yet predictivemodel for the charging of granular materials in collisionalflows based on straightforward dynamical systems reason-ing. We confirm the models predictions using discrete ele-ment simulations and a tabletop granular experiment.

Troy ShinbrotRutgers UniversityChemical & Biochem [email protected]

MS118

Entire Solutions for Lattice Differential Equationswith Obstacles

We construct entire solutions for scalar bistable lattice dif-ferential equations with obstacles in more than one spatialdimension. The method of proof is based on comparisonprinciples. The anisotropy in the lattice complicates theconstruction of super-solutions as compared with the PDEcase.

Aaron HoffmanFranklin W. Olin College of [email protected]

Hermen Jan HupkesUniversity of LeidenMathematical [email protected]


MS118

Positive Stationary Solutions and SpreadingSpeeds of KPP Equations in Locally Spatially In-homogeneous Media

This paper mainly explores spatial spread and front propa-gation dynamics of KPP evolution equations with randomor nonlocal or discrete dispersal in unbounded inhomoge-neous and random media and reveals such an importantbiological scenario: the localized spatial in-homogeneity ofthe media does not prevent the population to persist andto spread, moreover, it neither slows down nor speeds upthe spatial spread of the population. This is joint workwith Dr. Wenxian Shen.

Liang Kong, Wenxian ShenAuburn [email protected], [email protected]

MS118

Transition Fronts in Lattice Differential Equations

The purpose of this talk is two-fold. First we will providean overview of the talks in both Part I and Part II of thisminisymposium. Second we consider transition fronts forlattice differential equations in the presence of obstacles.Our interest is in both bistable and monostable dynamics.This is joint work with M. Brucal-Hallare, A. Hoffman,H.J. Hupkes, and A. Zhang.


MS119

Information Geometry and its Application in SpaceTracking

Information geometry seeks to study the geometric struc-ture of probability density function spaces. It is partic-ularly useful when the uncertain system subject to studyis neither Cartesian nor Gaussian. These features render

DS13 Abstracts 213

Cartesian and Gaussian classical approaches to uncertaintypropagation ineffective. An example of such systems istracking of space objects that satisfy Hamiltonian dynam-ics. This talk investigates the relationship between Hamil-tonian dynamics-based uncertainty propagation and thatdictated by the geodesic equation from information geom-etry.

Islam HusseinWorcester Polytechnic [email protected]

MS119

Symplectic Constraints with Applications to Space-craft Navigation

We begin with an overview of symplectic constraints inHamiltonian dynamical systems. We then discuss new re-sults on the evolution of time-dependent symplectic cross-sections found in tube invariants of normally hyperbolic in-variant manifolds, such as the libration points in the classicthree-body problem. Finally, we discuss how these resultsmight be applied to interplanetary space-mission design.

Jared M. MaruskinSan Jose State [email protected]

MS119

Symplectic Semiclassical Wave Packet Dynamics

I will talk about the geometry and dynamics of semiclassi-cal wave packets, which provide a description of the tran-sition regime from quantum to classical mechanics. I willshow how to formulate semiclassical mechanics from thesymplectic-geometric point of view by exploiting the geo-metric structure of quantum mechanics; this approach ef-fectively “strips away” quantum effects from quantum me-chanics and incorporates them into the classical descriptionof mechanics.

Tomoki OhsawaUniversity of MichiganDepartment of [email protected]

Melvin LeokUniversity of California, San DiegoDepartment of [email protected]

MS119

Mapping Probability Distributions Nonlinearly inSymplectic Dynamical Systems

The dynamical evolution of probability distributions insymplectic dynamical systems are studied, with an empha-sis on systems mapped by Hamiltonian Dynamics. Fun-damental conservation laws and constraints for symplec-tic systems are expressed in tangible ways for probabil-ity distributions, these include Liouvilles Theorem, Gro-movs Non-Squeezing Theorem, and the Integral Invariantsof Poincare-Cartan. These connections lead to implicationsand applications for the prediction of deterministic systemswith uncertain initial conditions.

Daniel ScheeresUniversity of Colorado, [email protected]

MS120

Diffusion-mapped Delay Coordinates for TimeScale Separation

An under-appreciated fact about attractor reconstructionis that the induced geometry of time-delay coordinates in-creasingly biases the reconstruction toward the stable di-rections as delays are added. This bias can be exploited,using the diffusion maps approach to dimension reduc-tion, to extract dynamics on desired time scales from high-dimensional observed data. We discuss the technique andits application to video data from experiments.

Tyrus BerryGeorge Mason [email protected]


MS120

Diffusion Maps as Invariant Functions of Dynami-cal Systems

We apply diffusion maps to obtain a representation of theergodic quotient of a dynamical system. The ergodic quo-tient is the joint image set of all flow-invariant functions,numerically approximated by averages of Fourier harmon-ics along trajectories. The dominant elements of the dif-fusion map act as flow-invariant functions whose level-setsare invariant regions of homogeneous dynamics, e.g., re-sembling integrable systems. We discuss the potential touse diffusion geometry in obtaining a model-free bifurca-tion analysis.

Marko BudisicDepartment of Mechanical EngineeringUniversity of California, Santa [email protected]


MS120

Diffusion Embeddings of Parameterized DifferenceEquations

In this talk I will present some results on how one can usediffusion maps to embed parameterized difference equa-tions. As the parameters of the difference equation arechanged, the geometry of the system changes as well. Injoint work with Ronald Coifman and Roy Lederman, weuse a single low dimensional embedding space to trackchanges in the intrinsic geometry of the system as the pa-rameters are changed.

Matthew J. HirnUniversity of MarylandCollege [email protected]

Roy LedermanYale [email protected]

Ronald Coifman

214 DS13 Abstracts

Yale UniversityDepartment of Computer [email protected]

MS120

Diffusion Maps for Model Reduction of Dynamicswith Symmetries

In the first part of this talk we will review the diffusionmaps framework for non-linear dimensionality reduction ofdata. We then introduce vector diffusion maps, which isa recent generalization of diffusion maps that is based onvector fields instead of scalar functions, and is particularlyuseful for data with underlying symmetries, with and with-out dynamics.

Amit Singer, Ioannis KevrekedisPrinceton [email protected], [email protected]

MS121

Cascades in Interdependent Networks


Raissa D’SouzaUC [email protected]

MS121

Approximation Methods for Dynamics on Net-works

I will briefly review several analytical approaches for dy-namics on networks, with a special focus on cascade dy-namics.

James P. GleesonUniversity of LimerickDept. of Mathematics and [email protected]

MS121

Limited Imitation Social Contagion as a Model ofFashions

We study binary state contagion dynamics on a social net-work where nodes act in response to the average state oftheir neighborhood. We model the competing tendenciesof imitation and non-conformity by incorporating an off-threshold into standard threshold models of behavior. Inthis way, we attempt to capture important aspects of fash-ions and general societal trends. Allowing varying amountsof stochasticity in both the network and node responses, wefind different outcomes in the random and deterministicversions of the model. In the limit of a large, dense net-work, however, these dynamics coincide. The dynamicalbehavior of the system ranges from steady state to chaoticdepending on network connectivity and update synchronic-ity. We construct a mean-field theory for general randomnetworks. In the undirected case, the mean-field theorypredicts that the dynamics on the network are a smoothedversion of the average node response dynamics. We com-pare our theory to extensive simulations on Poisson randomgraphs with node responses that average to the chaotic tentmap.

Kameron D. Harris



Peter DoddsDepartment of Mathematics and StatisticsThe University of [email protected]

MS121

Dynamics on Modular Networks with Heteroge-neous Correlations


Sergey MelnikUniversity of Limerick, [email protected]

MS122

A Framework for Approximate Reduced Models ofMultiscale Systems with Nonlinear and Multiplica-tive Coupling

We develop a new framework for approximate reducedmodels of multiscale processes. This framework approxi-mates the parameterized coupling terms in a reduced modelthrough their first-order Taylor expansion, which, in turn,is computed via the Fluctuation-Dissipation theorem. Wedemonstrate computationally that this framework is suit-able for multiscale systems with nonlinear and multiplica-tive coupling.

Rafail AbramovDepartment of Mathematics, Statistics and ComputerScienceUniversity of Illinois at [email protected]

MS122

Local Learning of Stochastic Dynamical Systems

In Chemistry and Biology many people are interested insimulating how a system of molecules interacts over a largeperiod of time. In order to obtain a long path of themolecules in the system, the standard method is to com-pute all the forces between all the atoms at each time stepand move forward in time. Unfortunately this dynamicalsystem is very stiff, and so we have to take very small timesteps (on the order of 10−15 s). I will outline a proce-dure that uses machine learning techniques to automati-cally learn a SDE that well represents the dynamics of thesystem. The SDE we learn will no longer depend upon do-ing expensive force field computations and can take largertime steps.

Miles CrosskeyRensselaer Polytechnic [email protected]

MS122

Dimension Reduction in Systems with Moderate

DS13 Abstracts 215

Separation of Time Scales

We develop effective stochastic models for moderately sepa-rated ”slow-fast” systems by eliminating non-essential fastmodes. Two approaches of the stochastic mode-reductionstrategy are presented. One is to reduce the dimension ofthe original full system through a slow manifold, the otheris homogenization. We present some examples and numer-ical simulations motivated by the shallow-water equation.

Xingye KanIllinois Institute of [email protected]

MS122

Dynamics of Nanomagnets with Spin-transferTorques

Driving nanomagnets by spin-polarized currents offers ex-citing prospects in magnetoelectronics, but the response ofthe magnets to such currents remains poorly understood.We show that an averaged equation describing the diffusionof energy on a graph captures the low-damping dynamics ofthese systems, and agrees with experimental observations.We then extend this averaging technique to spatially ex-tended systems described by stochastic partial differentialequations.

Katherine NewhallCourant Institute of Mathematical ScienceNew York [email protected]

Eric Vanden-EijndenCourant InstituteNew York [email protected]

MS123

Modeling Age and Size Based Division of Labor inFire Ant Workers

The size of single-queen, or monogyne colonies of fire antmay contain as many as a quarter million of workers of var-ious sizes. Worker polymorphism in the fire ant (Solenopsisinvicta) is common and there is a correlation between thebody size/age and tasks of workers. Young workers tendto spend more time within the nest by feeding or groom-ing larvae/queen. As workers get older, their duties shiftfrom the brood-tending to foraging which is the most dan-gerous job of worker ants. Since the size of colony is theprimary factor to determine the survival of the queen, ifthe foragers are selected from all workers at random with-out regard to age, it would lower the average lifespan ofworkers. Therefore, more resources must be invested to-ward worker production. This means a reduction in sexualalate production. In this project, we construct models toexamine how the physical and temporal castes of workersaffect the colony size compared to a colony of random-ageforagers.

Erika AsanoDepartment of Environmental Science, Policy andGeographyUniversity of South Florida [email protected]

MS123

Disease Spread on Long Distance Travel Networks

Recent epidemics like the SARS outbreak and the 2009pandemic influenza A(H1N1) highlighted the role of theglobal human transportation network played in the world-wide spread of infectious diseases. We introduce an SIR-based model to describe the temporal evolution of an epi-demic in regions connected by long distance travel, suchas intercontinental flights. Literature study of revealedon-board transmission of influenza in flights even with aduration of less than 8 hours, hence we include the pos-sibility of transmission of the disease during travel. Weobtain that an age structured model where age is the timeelapsed since the start of the travel leads to a nonlinearsystem of functional differential equations. We determinesome fundamental properties of the model and the repro-duction number. We parametrize the model and use realdemographic and air traffic data for specific regions. Wevalidate our approach fitting the model to the first wave ofthe 2009 influenza pandemic.

Diana KniplBolyai InstituteUniversity of [email protected]

MS123

Age of Maturity and Threshold Phenomena in AgeDependent Populations

We consider an age structured population model having thespecial feature that the age of maturity of an individual ata given time depends on the history of the age of maturity,and the history of the population density, at that time.This is manifested as a threshold condition for the resourceconsumption of the immature population. Using this asmotivation, we are led to a more general situation whichtakes the form of an abstract algebraic delay-differentialsystem. We discuss the progress made on this project.This is work is the result of a collaboration with Dr. FeliciaMagpantay and Dr. Jianhong Wu.

Nemanja KosovalicDepartment of Mathematics and StatisticsYork [email protected]

MS123

Disease Permeability of a Dynamic Social Network

In this study, we investigate the capacity of a newly in-troduced infectious disease to destabilize a social contactprocess, and drive that process to a new steady state. Ini-tially, we estimate a set of social contact parameters atthe dyad level using empirical data from a well-studiedherbivore. We then validate rule performance in recaptur-ing empirically observed higher-order network propertiesthrough simulation of dynamic networks. Next, we exam-ine the interacting effects of transmission probability, vir-ulence, and infectious period on the efficiency with whicha disease spreads through a dynamic (and evolving) socialcontact network. Finally, we assess the capacity of the in-troduced disease to push the social contact process to anew steady state.

Kezia ManlovePenn State [email protected]

216 DS13 Abstracts

MS124

Synchronization of Small Networks of Electrochem-ical Oscillators on Macro- and Microscale

Experimental results are presented in which the dynamicalfeatures of 2-20 electrochemical oscillating units are charac-terized as the network properties of coupling between unitsare tuned. In a macroscopic design the coupling is inducedby cross-resistances between electrodes; in the lab-on-chipdesign the coupling is inherent determined by the geome-try of the cell. The effects of network topology on identi-cal synchronization, clustering, and formation of chimerastates are investigated.

Istvan Z. KissDept. of Chemistry, Saint Louis UniversitySaint Louis, [email protected]

Mahesh WickramasingheSaint Louis [email protected]

Yanxin JiaDepartment of ChemistrySaint Louis [email protected]

MS124

Realization of Chimera States in a Network of Me-chanical Oscillators

Chimeras are counterintuitive states where a populationof identical oscillators splits into two parts, with one syn-chronizing and the other oscillating incoherently. Whilemany theoretical studies have been performed, the originand role of chimeras in nature and technology has remainedelusive. We present the first purely mechanical realizationof chimeras and show that chimeras emerge naturally in acompetition of two antagonistic synchronization patterns,and analyze a model and its bifurcation scenarios in detail.

Erik Andreas MartensMax Planck Institute for Dynamics & [email protected]

Shashi ThutupalliDept. of Mech. & Aerospace Eng., Princeton UniversityPrinceton, [email protected]

Antoine Fourriere, Oskar HallatschekMax Planck Institute of Dynamics & [email protected],[email protected]

MS124

Quasiperiodic Dynamics in Ensemble of Nonlin-early Coupled Electronic Oscillators

We perform experiments with 72 electronic limit-cycle os-cillators with global nonlinear coupling. With increase ofcoupling we observe a desynchronization transition to aquasiperiodic state. In this state the mean field is, how-ever, non-zero, but the mean field frequency is larger thanfrequencies of all oscillators. We analyze effects of commonperiodic forcing of the ensemble and demonstrate regimes

when the mean field is entrained by the force whereas theoscillators are not.

Michael RosenblumPotsdam UniversityDepartment of Physics and [email protected]

Amirkhan Temirbayev, Yerkebulan Nalibayeval-Farabi Kazakh National UniversityAlmaty, [email protected], [email protected]

Zeinulla Zhanabaeval-Farabi Kazakh National [email protected]

Vladimir PonomarenkoInstitute of Radio-Engineering and Electronics, RASSaratov, [email protected]

MS124

Collective Dynamics of Self Propelled Droplet Pop-ulations

Self propelled particles (SPPs) typically carry their own en-ergy and are not propelled simply by the thermal buffetingdue to the environment. As non-equilibrium entities, theyare not restricted to classical equilibrium constrains. Wedeveloped microscale self-propelled droplets which can beproduced in large numbers and with high monodispersity,allowing us to perform experiments on large ensembles ofsuch SPPs. We will discuss their non-equilibrium statisti-cal mechanics and collective dynamics such as flocking andrectification.

Shashi ThutupalliDept. of Mech. & Aerospace Eng., Princeton UniversityPrinceton, [email protected]

Stephan HerminghausMax Planck Institute for Dynamics and [email protected]

MS125

Predator-prey Interactions Using Particle Models

We discuss an aggregation model of predator-prey interac-tions. In the absence of predators, prey are represented bya particle system for which the steady state consists of aswarm of uniform density. Adding a predator introducesinteresting dynamics into the system. We give some ana-lytical results concerning the shape of the resulting swarmand stability of the predator-prey interactions. Joint workwith Yuxin Chen.

Theodore KolokolnikovDalhousie [email protected]

MS125

Inferring Individual Rules Through the Dynamicsof Phase Transitions in Collective Motion

Connecting observations of collective motion in animal

DS13 Abstracts 217

groups to individual-based models usually involves aver-aging over time and space to obtain a clear signal fromeach for comparison. However, many dynamic processesrequire the temporal component to be maintained in or-der for models to shed light on the process. Here, I studythe evolution of order from disordered states in both mod-els, and in actual observations of collective motion in anaquatic duck, to (a.) determine signatures of the tran-sition, and (b.) determine what model components andparameters reproduce properties of the transition. We findevidence reinforcing previous observations on relative mag-nitudes of interaction forces in this biological system.

Ryan LukemanDepartment of Mathematics, Statistics and ComputerScienceSt. Francis Xavier [email protected]

MS125

Field Experiments and Tracking of Animal Groupsin 3d

The key to comprehend the mechanisms of collective ani-mal motion is to obtain quantitative empirical data of in-dividual trajectories of group members. We present newresults both for flocks of starlings and swarms of midgesrecorded in the field using a stereographic camera systemand tracked in the 3dimensional space using a built in homealgorithm. In this talk I will describe our experimentalsetup and show main results of the tracking algorithm.

Stefania MelilloInstitute for Complex Systems Sapienza University [email protected]

MS125

Emergent Dynamics of Laboratory Insect Swarms

Emergent collective behavior, in flocks, swarms, schools,or crowds, is exhibited throughout the animal kingdom.Many models have been developed to describe swarmingand flocking behavior using systems of self-propelled par-ticles obeying simple rules or interacting via various po-tentials. Little empirical data, however, exists for real bi-ological systems that could be used to benchmark thesemodels. To fill this gap, we report measurements of labo-ratory swarms of flying Chironomus riparius midges, usingstereoimaging and particle tracking techniques to recordthree-dimensional trajectories for all the individuals in theswarm. We present a statistical characterization of theemergent behavior of the swarms, as well as a characteri-zation of the small-scale interactions.

Nicholas T. OuelletteYale UniversityDepartment of Mechanical Engineering and [email protected]

MS126

Probabilistic Source Regions and the Role of La-grangian Coherent Structures

For many applications, particle back-trajectories are essen-tial. Recent results show that a new interpretation of theFTLE field can explain the varied origin of particles sam-pled sequentially at a geographically fixed location. By in-

cluding subgrid turbulence, a stochastic process, the notionof probabilistic source regions emerge. A related importantnotion is the persistent barrier, connected to instantaneoussaddle points of the Eulerian field, which may lead to themost diverse samples in terms of origins.

Amir Ebrahim Bozorg MaghamVirginia [email protected]


MS126

The Ecology of Mixing

Detailed understanding of biophysical transport in coastalupwelling systems is critical for effective ecosystem man-agement. Using an ocean model of the California Currentsystem, we discuss kinematics of patchiness generation forbuoyant Lagrangian particles (plankton). Particle aggrega-tion is strongly controlled by coherent structures and par-ticularly eddy merging. We review and compare metricsto quantify patchiness (or mixedness) of this biophysicalflow, including variance based and fractal metrics, whichgive surprisingly similar results for this system.

Cheryl HarrisonCollege of Earth, Ocean and Atmospheric ScienceOregon State [email protected]

MS126

Grand Lagrangian Deployment (glad): DispersionCharacteristics in the Northern Gulf of Mexico

Initial dispersion, residence time, and advective pathwayresults obtained from the nearly simultaneous deploymentof some 300 surface drifters in the vicinity of the DeSotoCanyon are reported. The goal of the GLAD experimentwas to characterize, with unprecedented statistical signifi-cance, multi-point and multi-scale dispersion properties ofthe flow in the region of the Deepwater Horizon spill site in-cluding demarcation of the advective pathways between theCanyon and larger-scale flow features in the Gulf. For theinitial time period considered, relative dispersion is foundto be controlled by local dynamics. Very limited exchange,either across-shelf or with nearby mesoscale features, wasobserved.

Tamay Ozgokmen

University of Miami/[email protected]

Andrew PojeCUNY / College of Staten [email protected]

Bruce LipphardtSMSP, University of Delaware, Newark DE [email protected]

Brian HausUniversity of [email protected]

218 DS13 Abstracts

Gregg [email protected]

Ad Reniers, M. Josefina Olascoaga, Edward Ryan,Guillaume NovelliUniversity of [email protected], [email protected],[email protected], [email protected]

MS126

Trajectory Complexity Methods and LagrangianCoherent Structures in 3D Fluid Flows

We consider methods for identifying Lagrangian coherentstructures (LCS) in both 2D and 3D geophysical fluid flowsusing individual trajectory complexities. Particulary twocomplexity methods - the correlation dimension and er-godicity defect - are discussed in the context of severalexamples. The theoretical and practical advantages anddisadvantages of the complexity methods in comparison toother standard methods is also discussed.

Sherry ScottDepartment of MathematicsMarquette [email protected]

Irina Rypina, Lawrence PrattWoods Hole Oceanographic [email protected], [email protected]

Mike BrownRSMASMiami [email protected]

MS127

Functional Relevance of Activity Propagation inV1

Combining optical imaging of voltage-sensitive dye inawake behaving monkey with appropriate denoising andsignal processing methods, we prove the existence of ac-tivity propagation at single-trial level. Such propagationsgenerate dynamic lateral interactions within cartographicrepresentations that have strong functional implications.For instance, interactions between feedforward waves ofactivity and lateral interactions can be at the origin ofcontext-dependent dynamic input normalization linked tothe emergence of global mesoscopic signal.

Frederic ChavaneCNRSInstitut de Neurosciences de la [email protected]

Alexandre ReynaudMc Gill [email protected]

Lyle Muller, Alain DestexheCNRS [email protected], [email protected]

MS127

Complex Oscillatory Patterns in a Neuronal Net-

work with Adaptation and Lateral Inhibition

Recent studies of a firing rate model for two mutually in-hibitory neuronal populations show the existence of sev-eral dynamical regimes, including mixed-mode oscillations.We extend these results to a spatially distributed networkcharacterized by local excitatory and long-range inhibitoryconnections and firing rate neuronal adaptation. We showthat intricate spatio-temporal patterns derived from themixed-mode solutions seen in the reduced model can occurin certain parameter regimes.

Rodica CurtuUniversity of IowaDepartment of [email protected]

MS127

Spatially Coherent Dynamics in a Pair of Interact-ing Neural Field Layers

Given the ubiquity of interconnected regions in the brain,we present a model for a pair of interacting neural fieldlayers which could represent two different reciprocally con-nected layers of brain tissue, brain regions, or pools of neu-rons within the same layer. We study the existence andstability of stationary solutions and explore bifurcationsto stationary and spatially-coherent oscillatory solutionsin neural fields with excitation and inhibition, includingeffects of adaptation and inhomogeneous inputs.

Stefanos FoliasDepartment of Mathematical SciencesUniversity of Alaska [email protected]

MS127

Waves in Random Neural Media

While travelling waves in homogeneous neural media arerelatively well-studied, little work has been done on spa-tially and/or temporally heterogeneous media. I will showsome recent results in this direction obtained using numer-ical techniques developed for the study of stochastic partialdifferential equations.

Carlo R. LaingMassey [email protected]

MS128

Controlling Collective Behavior

A key problem is how to apply a efficient control strate-gies so that a network dynamics is exploited to obtain adesired ordered collective behavior. In this talk, we ad-dress this issue and also present an adaptive decentralizedpinning control technique that impose a desired dynamicsto the network. We also assess the interplay between thesynchronization state stability and the controller action toachieve the desired controlled dynamics.

Elbert E. MacauINPE - Brazilian National Institute for Space ResearchLAC - Laboratory for Computing and [email protected]

DS13 Abstracts 219

MS128

Do the Functional Networks Reveal the StructuralOrganization?

Experimental results typically do not access the networkstructure, which is then inferred by the node dynamics.From the dynamics one constructs a network of functionalrelations, termed functional network. A fundamental ques-tion towards the understanding of complex systems con-cerns the relation between functional and structural net-work. We show that the functional network can drasti-cally differ from the topological network. We uncover themechanism for this abrupt change between functional andstructural networks.

Tiago PereiraDepartment of MathematicsImperial College, London, [email protected]

MS128

Dynamics of Synchronous Neurons

Neural synchronization is of interest in the stages of sleep-ing, seizures, Parkinsons disease, depression, and more.Here we (1) describe neuron model equations based on theHuber and Braun (HB) work, (2) show their wide rangefiring regimes, (3) discuss how these neurons develop pat-terns of synchronous behavior, and (4) extend the modelto the multi-compartment case applied to the crab stom-atogastric neural system.


MS128

How to Select Neighbors for Robust Consensus

Network topology plays a critical role in collective be-haviour, influencing the outcome, speed and robustness ofgroup decision-making. We gain insight into the effects of adirected communication network on robustness of consen-sus to noise by extending the notion of effective resistancefrom undirected graphs. This allows us to relate structuralfeatures of the directed graph to the group robustness andderive rules by which individuals can change their neigh-bours to improve performance.

George F. YoungDepartment of Mechanics & Aerospace EngineeringPrinceton University, Princeton, [email protected]

Luca ScardoviDepartment of Electrical and Computer EngineeringUniversity of [email protected]

Naomi E. LeonardPrinceton [email protected]

MS129

Turing Patterns for Nonlocal Diffusive Systems

Many physical and biological processes occur with long-

range interaction, giving rise to nonlocal in space opera-tor equations. These operators are diffusive-like but arebounded rather than unbounded as is the case of the diffu-sion operator. We study systems which include such nonlo-cal operators and show that Turing instabilities also occur,producing patterned stable states.

Peter W. BatesMichigan State UniversityDepartment of [email protected]

Guangyu ZhaoUniversity of The West Indies, [email protected]

MS129

Solitary Waves in the FPU Chain: A New ExactSolution

We consider solitary wave solutions in the Fermi-Pasta-Ulam problem with piecewise linear nearest-neighbor inter-actions. We show that in this case the problem reduces toa Fredholm integral equation of the second kind, which canbe solved explicitly using the Wiener-Hopf method. Takingadvantage of the availability of an exact solution, we testthe limits of applicability of the simplest quasicontinuumapproximations of the discrete problem. We show thatin agreement with the results of Friesecke and Matthies(2002), atomic-scale localization occurs in the high-energylimit. Numerical simulations suggest stability of the ob-tained solutions above a certain velocity threshold.

Lev TruskinovskyLaboratoire de Mechanique des SolidesEcole [email protected]

Anna VainchteinDepartment of MathematicsUniversity of [email protected]

MS129

Traveling Wave Solutions with Mixed Dispersal forSpatially Periodic Fisher-KPP Equations

Traveling wave solutions to a spatially periodic nonlo-cal/random mixed dispersal equation with KPP nonlin-earity are studied. By constructions of super/sub solu-tions and comparison principle, we establish the existenceof traveling wave solutions with all propagating speedsgreater than or equal to the spreading speed in every di-rection. For speeds greater than the spreading speed, wefurther investigate their uniqueness and stability.

Aijun ZhangUniversity of [email protected]

MS130

Topological Changes in Chaotic Invariant Sets

In this talk we reveal the existence of a new codimension-1curve that involves a topological change in the structureof the chaotic invariant sets (attractors and saddles) ingeneric dissipative systems with Shilnikov saddle-foci. Thiscurve is related to some spiral-like structures that appear

220 DS13 Abstracts

in the biparameter phase plane. We show how this curveconfigures the spiral structure (via the doubly-superstablepoints) originated by the existence of Shilnikov homoclin-ics and how it separates two regions with different kind ofchaotic attractors or chaotic saddles. Inside each region,the topological structure is the same for both, chaotic at-tractors and saddles.

Sergio Serrano, Roberto BarrioUniversity of Zaragoza, [email protected], [email protected]

Fernando BlesaUniversity of [email protected]

MS130

Global Study of 2D Dissipative Diffeomorphismswith a Homoclinic Figure-eight

We consider 2D diffeomorphisms having a homoclinicfigure-eight to a dissipative saddle. We study the rich dy-namics that they exhibit under a periodic forcing. Generi-cally the manifolds split and undulate giving rise to a largebifurcation diagram. Many tools to study it and to detectthe (co)existent attractors will be presented. The quali-tative description of the global dynamics in a fundamen-tal domain is complemented with the analysis of a returnmodel that provides quantitative data.

Arturo VieiroUniversity of [email protected]

Sergey V. GonchenkoUniversity of Nizhny [email protected]

Carles SimoUniversity of [email protected]

MS130

Symbolic Tools for Deterministic Chaos

Computational technique based on the symbolic descrip-tion utilizing kneading invariants is proposed for explo-rations of parametric chaos in three exemplary systemswith the Lorenz attractor: the iconic Lorenz equationsfrom hydrodynamics, the Shimizu-Morioka model - a nor-mal model from mathematics, and a laser model from non-linear optics. The technique allows for uncovering the stun-ning complexity and universality of the patterns discoveredin the bi-parametric scans of the given models and de-tects their centers organizing a plethora of spiral structurescodimension two T(erminal)-points and separating saddlesin intrinsically fractal regions corresponding to complexchaotic dynamics.

Tingli XingGeorgia State [email protected]

Jeremy [email protected]



MS131

A Practical Mathematical Model of IntermittentAndrogen Suppression for Prostate Cancer

Prostate cancer is an ideal target for preparing mathemat-ical tools to treat diseases because there is a commonlyused tumor marker and a good but temporarily effectivehormone therapy. In this talk, we summarize the recentadvancements of mathematical modeling of prostate can-cer. Our special focus is on robustly personalizing a treat-ment schedule of intermittent androgen suppression. Somegeneral mathematical problems that should be consideredin the future will be also discussed.

Yoshito HirataInstitute of Industrial ScienceThe University of [email protected]

Koichiro AkakuraDepartment of Urology, Tokyo Kosei Nenkin Hospital,[email protected]

Celestia HiganoDepartment of Medicine, University of Washington andFred Hutchinson Cancer Research [email protected]

Nicholas BruchovskyVancouver General [email protected]

Kazuyuki AiharaJST/University of Tokyo, JapanDept of Mathematical [email protected]

MS131

A Model of Personalized Androgen Ablation Ther-apy for Metastatic Prostate Cancer

Metastatic prostate cancer is treated with continuous an-drogen ablation. However, this approach eventually failsdue to progression to a castration-resistant state. Here, wepresent a biochemically-motivated model of prostate cancergrowth that incorporates a number of personalized param-eters. The model is used to retrospectively analyze patientcase histories in order to: (i) investigate the benefits ofcontinuous versus intermittent androgen ablation; and (ii)to evaluate the potential of these parameters as biomarkersfor significant disease.

Harsh JainMathematical Biosciences InstituteThe Ohio State [email protected]

DS13 Abstracts 221

MS131

Immunotherapy with Androgen Deprivation Ther-apy May Stabilize Prostate Cancer

A mathematical model of advanced prostate cancer treat-ment is developed to examine the combined effects ofandrogen deprivation therapy and immunotherapy. Themodel presented in this paper examines the efficacy of den-dritic cell vaccines when used with continuous or intermit-tent androgen deprivation therapy schedules. Numericalsimulations of the model suggest that immunotherapy cansuccessfully stabilize prostate cancer growth using eithercontinuous or intermittent androgen deprivation.

Yang KuangArizona State UniversityDepartment of [email protected]

MS131

The Evolution of Androgen-receptor Expression inProstate Cancer

In previous research we investigated natural selection act-ing on androgen receptor expression in prostate cancer us-ing a multi-scale model. This model outlined conditionsunder which aggressive, hormone-resistant tumors arise.Here we extend the model by generalizing its strategy spaceto allow androgen expression to vary continuously. We an-alyze the extended model using adaptive dynamics. Theresults of this extended model are used to refine the pre-dictions of the original investigation.

John D. NagyScottsdale Community CollegeArizona State [email protected]

Steffen EikenberryKeck School of MedicineUniversity of Southern [email protected]

Yang KuangArizona State UniversityDepartment of [email protected]

MS132

Evolution Systems on Time-dependent Domains:Study of Dynamics, Stability, and Coarsening

In this talk we discuss the key differences in the stabil-ity picture between extended systems on time-fixed andtime-dependent spatial domains. As a paradigm, we usethe complex Swift-Hohenberg equation to study dynamicpattern formation and evolution on time-dependent spa-tial domains. In particular, we discuss the effects of atime-dependent domain on the stability of spatially ho-mogeneous and spatial periodic base states as well as onpattern coarsening.

Rouslan KrechetnikovDepartment of Mechanical EngineeringUniversity of California at Santa [email protected]

Edgar KnoblochUniversity of California at Berkeley

Dept of [email protected]

MS132

Front Motion, Pinning and Depinning in One andTwo Spatial Dimensions

The 1:1 forced complex Ginzburg-Landau equation ex-hibits bistability between spatially homogeneous equilib-ria and thus admits traveling fronts in both one and twodimensions. When one equilibrium becomes Turing unsta-ble, the front can be pinned to Turing patterns (e.g. rollsand hexagons) bifurcating from this equilibrium. Depin-ning processes outside the parameter interval of pinninginvolve stretching of the pattern wavelength accompaniedby creation or destruction of cells at a preferred distancefrom the front.

Yi-Ping MaUniversity of Chicago, Department of GeophysicalSciencesChicago, IL 60615 [email protected]


MS132

Linear Stability of Time-dependent Flows

We present a general theory and two examples for the lin-ear stability of non-autonomous systems and present twoexample of its use. The technique essentially identifies thespectral radius of the propagator of the linear operatoras the appropriate measure for the amplification of initialperturbations by the linearized dynamics. The techniqueconnects and generalizes the classical modal stability the-ory using eigenvalues and the non-modal approaches usingoptimal growth of energy.

Shreyas MandreBrown University, School of Engineering184 Hope Street, Box D, Providence RI 02912shreyas [email protected]

Xinjun GuoBrown Universityxinjun [email protected]

Anja SlimSchlumberger-Doll Research centerCambridge [email protected]

MS132

Dynamic Bifurcations and Melting-boundary Con-vection

This talk focuses on a simple physically motivated modelof time-dependent changes in stability. The talk presentsa model for weakly nonlinear thermal convection in a fluidlayer with a melting top boundary. This leads to the deriva-tion of a new set of non-autonomous envelope equationsas a dynamic generalization to the well-known Ginzburg-Landau equation. However, because of the interaction oftwo destabilizing mechanisms (convection and morpholog-

222 DS13 Abstracts

ical dynamics), this new system possesses a number of in-teresting properties not found in systems close to a tradi-tional dynamic bifurcation. The presentation will highlightsome of the properties of this system both analytically andnumerically; specifically, we’ll find the robust “locking in’of spatially complex patterns, and show this is a generalfeature of systems of this nature.

Geoffrey M. VasilCanadian Institute for Theoretical Astrophysics, Uni60 St. George Street, Toronto, ON, Canada M5S [email protected]

Michael ProctorDAMTPUniversity of [email protected]

MS133

How Do Cells Detect the Frequency of PulsatileChemical Signals?

A hallmark of the endocrine system is pulsatile hormonesecretion. Target cells often respond to pulsatile hormonesdifferentially depending on pulse frequency. To distin-guish responses to pulse frequency from responses to chang-ing hormone dose, we consider the frequency response oftarget cells to a family of dose normalized input signals.We show that simple nonlinear feedforward systems canshow increasing, decreasing, or non-monotonic frequencyresponses to pulsatile signals with constant mean dose.

Patrick A. FletcherDepartment of MathematicsFlorida State University, Tallahassee, [email protected]

Joel TabakDept of Biological SciencesFlorida State [email protected]

Richard BertramDepartment of MathematicsFlorida State [email protected]

MS133

(Exploiting the) Fast and Slow Time Scales in Cel-lular Signalling

Oscillations and bursts act as signals in many cell types,including those involved in neuronal firing and cell secre-tion. A key feature of the dynamics in there cells is thatsome physiological processes evolve much faster than oth-ers. We can take advantage of this separation in timescalesto analyse models using geometric singular perturbationtechniques. These techniques allow us to explain ‘tran-sient’ responses as well as long-term dynamics by identi-fying canards and invariant manifolds that organise thephasespace.

Emily HarveyUniversity of [email protected]

MS133

Population Spiking Dynamics and Signal Process-

ing in Vasopressin Neurons

The magnocellular vasopressin neurons of the hypothala-mus act to maintain osmotic pressure by regulating kidneyfunction. Experiments show a robust linear relationshipbetween osmotic pressure and vasopressin hormone secre-tion despite the very non-linear properties of spike gen-eration and stimulus-secretion coupling in the vasopressinneurons. Here we simulate the spiking and secretion mech-anisms, and use a population model to examine how cellheterogeneity interacts with the spiking and secretion prop-erties to produce a linear population response.

Duncan J. MacGregor, Gareth LengCentre for Integrative PhysiologyUniversity of [email protected], [email protected]

MS133

Modeling the Glucagon Secreting Alpha Cell

While pancreatic β-cells release insulin in response to highglucose levels, α-cells release glucagon when blood glucoseis low. Both insulin and glucagon work together to main-tain glucose homeostasis. While the mechanisms leading toinsulin secretion are fairly well understood, how glucagonsecretion is suppressed at high glucose levels is still de-bated. We developed a mathematical model of the α-celland investigated intrinsic mechanisms that lead to the sup-pression of glucagon secretion.

Margaret A. WattsDepartment of MathematicsFlorida State [email protected]

Arthur ShermanLaboratory of Biological ModelingNational Institutes of [email protected]

MS134

Heterogeneity and Correlation Transfer in Noise-Driven Oscillators

We consider the ability of two uncoupled heterogeneous os-cillators to synchronize when driven with colored partiallycorrelated noise. We derive equations for the stationarydensity of the phase difference assuming small noise andfind two surprising results :

1. at low correlations it is possible for pairs of heteroge-neous oscillators to synchronize better than a pair ofhomogeneous oscillators;

2. if the oscillators have different frequencies, there is anonzero time scale of the noise that maximizes syn-chrony

Bard ErmentroutUniversity of PittsburghDepartment of [email protected]

Pengcheng ZhouCarnegie Mellon [email protected]

MS134

Infering Phase Dynamics from Observations of Os-

DS13 Abstracts 223

cillatory Networks

It is described, how the interconnections in a network ofcoupled oscillators can be detected from the processing ofthe observed multivariate time series. The procedure sug-gested leads to invariant description in terms of phases,independent on the obseravbles and embeding used, anddelivers phase equations in the form used in theory. Themethod is illustrated with the analysis of experimentaldata.

Arkady PikovskyDepartment of PhysicsUniversity of Potsdam, [email protected]

Michael RosenblumPotsdam UniversityDepartment of Physics and [email protected]

MS134

Geometry of Irregular Oscillations and Applica-tions

Phase of irregular oscillations in nonlinear and non-equilibrium systems becomes arbitrary with fluctuationsin amplitude. The problem amounts to correctly iden-tifying those system states that are in the same phase.For limit-cycle oscillators, states are identified by hyper-surfaces called isochrones. We propose a generalization ofisochrones for an application to irregular oscillations. Thedynamics of the resultant phase is on average decoupledof the amplitude dynamics. The approach is illustrated byapplications to pulmonary respiration.

Justus C. SchwabedalDivision of Sleep Medicine, Brigham & Women’s HospitalHarvard Medical [email protected]

MS134

Bifurcations of Bursting Polyrhythms in 3-CellCentral Pattern Generators

We identify and describe the principal bifurcations ofbursting rhythms in multifunctional central pattern gen-erators (CPG) composed of three neurons connected byfast inhibitory or excitatory synapses. We develop a set ofcomputational tools that reduce high-order dynamics in bi-ologically relevant CPG models to low-dimensional returnmappings that measure the phase lags between cells. Weexamine bifurcations of fixed points and invariant curvesin such mappings as coupling properties of inhibitory andexcitatory synapses are varied. These bifurcations corre-spond to changes in the availability of the network’s phaselocked rhythmic activities such as periodic and aperiodicbursting patterns. As such, our findings provide a system-atic basis for understanding plausible biophysical mecha-nisms for the regulation of, and switching between, motorpatterns generated by various animals.


Jeremy Wojcik, Aaron KelleyGSU

[email protected], [email protected]

Robert ClewleyGeorgia State UniversityDepartment of Mathematics and Statistics, [email protected]

MS135

Sensory Encoding Mechanisms in Neuronal Dy-namics

In sensory systems, it has been widely observed that recep-tor cells outnumber the neurons in the immediate down-stream layer by several orders of magnitude. Thus, a nat-ural question to ask is how much information is lost be-cause of this reduction? We answer this question usingcompressed sensing theory as a tool for quantifying infor-mation retention in an idealized retinal model. Via numeri-cal simulations and mathematical analysis, we demonstrateseveral necessary conditions for data compression.

Victor BarrancaRensselaer Polytechnic [email protected]

Gregor KovacicRensselaer Polytechnic InstDept of Mathematical [email protected]

David CaiNew York UniversityCourant [email protected]

MS135

Low-dimensional Descriptions of Neural Networks

Biological neural circuits display both spontaneous asyn-chronous activity, and complex, yet ordered activity whileactively responding to input. When can model neural net-works demonstrate both regimes? Recently, researchershave demonstrated this capability in large, recurrently con-nected neural networks, or “liquid state machines”, withchaotic activity. We study the transition to chaos in a fam-ily of such networks, and use principal orthogonal decom-position techniques to provide a low-dimensional descrip-tion of network activity. We find that key characteristics ofthis transition depend critically on whether a fundamentalneurobiological constraint — that most neurons are eitherexcitatory or inhibitory — is satisfied.

Andrea K. BarreiroDepartment of Applied MathematicsUniversity of [email protected]

MS135

Information Transmission in Discrete FeedforwardNetworks

We study the emergence of neutral stability and rate prop-agation in stochastic feedforward networks. Spectral prop-erties of a mean-field approximation can reveal when com-plex dynamics and high levels of information transmissionco-occur in these networks. A key issue is robustness toconnection parameters, which can be improved by adding

224 DS13 Abstracts

biological factors such as noise and inhibition. We fur-ther examine how biophysically motivated learning rulescan control network connectivity to improve informationtransmission.

Natasha A. Cayco Gajic, Yoni Browning, EricShea-BrownUniversity of WashingtonDepartment of Applied [email protected], [email protected], [email protected]

MS135

Wave Patterns in an Excitable Neuronal Network

This talk describes a study of spiral- and target-like wavestraveling in a two-dimensional network of integrate-and-fireneurons with close-neighbor coupling. Individual neuronsare driven by Poisson spike trains. Waves begin as a targetor a spiral, and evolve into a straight ”zebra”-like grat-ing. The wavelength and wave speed of the patterns wereinvestigated, as were the temporal power spectra of the os-cillations experienced by the individual neurons as waveswere passing through them.

Christina H. LeeRollins CollegeRensselar Polytechnic [email protected]

MS136

Multistable Dynamics of Stochastically SwitchingNetworks

We consider multistable dynamical networks whose con-nections switch stochastically according to a given rule.The stochastic switching can be a sequence of independentrandom vectors or a Markov vector process. We study dy-namical properties of the multistable switching networksas a function of the switching frequency. We also analyzehow the switching network topology of dynamical networkscan enhance the performance of networks with static con-nections.

Igor BelykhDepartment of Mathematics and StatisticsGeorgia State [email protected]

MS136

On Convergence and Synchronization in PiecewiseSmooth Networks

Switching in complex networks can be undesired whenthe goal is to guarantee emergence of coordinated mo-tion. Conversely, it can be usefully exploited to designdistributed control laws for the emergence of desired coor-dinated behaviour. We consider hybrid-switched networksof dynamical systems and present new tools to study con-vergence of all agents towards the same evolution. Weuse these tools to develop novel switched strategies to con-trol the emergence and properties of such coordinated be-haviour.

Davide LiuzzaUniversity of Naples Federico [email protected]

Mario Di BernardoUniversity of Bristol

Dept of Engineering [email protected]

MS136

Neighborhood Gossip: Exploiting Structure inMoving Neighborhood Networks to DiscoverGlobal Environmental Variables

We consider a network of mobile agents that act as pointenvironmental sensors, where agents communicate only lo-cally. Suppose the network task is to approximately de-scribe some enviromental state over the domain of move-ment, where typically global information is required (suchas transport problems). We describe techniques to exploitthe Moving Neighborhood Network structure and topologyto resolve the function using local processing information.

Joseph SkufcaClarkson [email protected]

MS136

Information Transfer in Coupled Oscillator Net-works: Uncertainty, Influence, and Effects of Blink-ing Channels

Causality inference is central in nonlinear time series anal-ysis. A popular approach to infer causality between twoprocesses is to measure the information transfer betweenthem, a notion termed as transfer entropy. Using networksof coupled oscillators, we show that the presence of indirectinteractions, common drivers, and blinking channels oftenresults in erroneous identification of network connections.We overcome these limitations by developing an entropyreduction approach, whose effectiveness is tested againstvarious networks.

Jie Sun, Erik BolltClarkson [email protected], [email protected]

PP0

The Tranport Through Nontwist Barriers in aModel Describing Magnetic Field Lines in Toka-maks

We use a symplectic map to model magnetic field lines intokamaks perturbed by ergodic magnetic limiter. Partic-ularly, we are interested in the transport of trajectoriesunder the influence of nonmonotonic safety factor profiles,leading to nontwist scenarios characterized by the pres-ence of a robust invariant torus (shearless). In the presentwork we study a parameter space profile and the shearlessbreakup that marks the onset of the transport of trajecto-ries towards the boundary.

Celso AbudUniversity of Sao [email protected]

Ibere L. CaldasInstitute of PhysicsUniversity of Sao [email protected]

PP0

Dynamics of Short Desynchronization Episodes in

DS13 Abstracts 225

the Brain

While neural synchronization is widely observed in neuro-science, neural oscillations are rarely in perfect synchronyand go in and out of phase in time. We found that neu-ral synchronization in different circuits of the brain fol-lows qualitatively similar temporal pattern: desynchro-nization episodes are very short, but frequent. We explorethe mechanisms responsible for these patterns in simpleconductance-based models. We show that short desyn-chronizations may allow for higher levels of synchrony withweaker synaptic connections.

Sungwoo AhnIndiana University Purdue University [email protected]

Leonid RubchinskyDepartment of Mathematical SciencesIndiana University Purdue University [email protected]

PP0

Localized Pattern in Periodically Forced Systems

Oscillons, spatially localized oscillatory patterns, were dis-covered in the Faraday wave experiment in the 1990s. Wereduce a simple model PDE [A.M.Rucklidge & M.Silber,SIADS 8 (2009) 298-347] with parametric forcing tothe forced complex Ginzburg-Landau equation where itis known [J.Burke, A.Yochelis & E.Knobloch, SIADS 7(2008) 651-711] that oscillons can be found, and are able todemonstrate a quantitative connection between the oscil-lons found numerically in the model PDE and those fromthe forced complex Ginzburg-Landau equation.

Abeer Al-NahdiUniversity of [email protected]

PP0

The Swarm and the Mosquito: Information Trans-fer, Co-Operation and Decision Making in a Group

Mosquitoes form swarms which serve selected functionsduring mating behavior. Males fly together in a “coher-ent’ group, which attracts the attention of nearby females.Communication between individuals is observed to rely onacoustic interaction; each mosquito dynamically adjusts itswing beat frequency in response to the sound of its neigh-bors. We present experimental data investigating the na-ture of these interactions, and discuss them in the broadercontext of swarm structure, dynamics and stability.

Andy AldersleyUniversity of [email protected]

Martin HomerUniversity of BristolEngineering Mathematics [email protected]

Alan R. Champneys, Daniel RobertUniversity of [email protected], [email protected]

PP0

Algorithm for Interval Linear Programming Involv-ing Interval Constraints*

In real optimization, we always meet the criteria of usefuloutcomes increasing or expenses decreasing and demandsof lower uncertainty. Therefore, we usually formulate anoptimization problem under conditions of uncertainty. Inthis paper, a new method for solving linear programmingproblems with fuzzy parameters in the objective functionand the constraints based on preference relations betweenintervals is investigated. To illustrate the efficiency of theproposed method, a numerical example is presented.

Ibraheem AlolyanKing Saud [email protected]

PP0

Travelling Waves in a Fractional Fisher EquationUsing the Homotopy Analysis Method

In this poster, the Homotopy Analysis Method (HAM),which is a powerful tool to solve nonlinear equations andoriginally proposed by Liao, is applied to traveling waves inthe fractional Fisher equation. Different from traditionalperturbation techniques, HAM does not rely on small pa-rameters. HAM makes use of an auxiliary convergence pa-rameter to provide an efficient way to determine the con-vergence region of the series. Numerical examples are givento support the idea.

Inan Ates, Paul A. ZegelingDept. of MathematicsUtrecht [email protected], [email protected]

PP0

Mesoscale Symmetries Explain Dynamical Equiva-lence of Food Webs

A goal of complex system research is to identify dynam-ical implications of network structure, such as small mo-tifs influencing the dynamics on the network as a whole.Here, we investigate ecological food webs, complex hetero-geneous networks of interacting populations. We show thatcertain mesoscale symmetries imply the existence of local-ized dynamical modes. If unstable they cause dynamicalinstability regardless of the embedding network; if stabletheir removal results in a smaller but dynamically equiva-lent network.

Helge AufderheideUniversity of Bristol,Merchant Venturers School of [email protected]

Lars RudolfUniversity of BristolMV School of Math [email protected]

Thilo GrossUniversity of Bristol, [email protected]

PP0

Investigating Physical Experiments with Control-

226 DS13 Abstracts

Based Continuation

We present a general method for systematically investi-gating the dynamics and bifurcations of a physical non-linear experiment. In particular, we show how the odd-number limitation inherent in a popular non-invasive con-trol scheme, (Pyragas) time-delayed feedback control, canbe overcome for experiments with periodic forcing. Todemonstrate the use of our non-invasive control, we traceout experimentally the resonance surface of a nonlinearoscillator near the onset of instability, around two saddle-node bifurcations (folds) and a cusp bifurcation.

David A. BartonUniversity of Bristol, [email protected]


PP0

Analysis of Fluid Systems from the Optical Flow-Approximate Vector Fields

Analysis of fluid systems such as the ocean and atmosphereis important topics in current research. To analyze globaldynamics of such systems, such as coherent pairs and trans-port barriers, the vector fields of the systems are required.In the absence of a prior model, multi-time step opticalflow technique can be employed on remote data to deter-mine the vector fields. In this work, the transport barriersfor the Jupiters atmospheric data are explained.

Ranil Basnayake, Erik BolltClarkson [email protected], [email protected]

PP0

Spatiotemporal Dynamics of Alternans Nodes inHeterogeneous Cardiac Tissue

We study the behavior of electrical alternans, a period-2 cardiac rhythm resulting in beat-to-beat alternations inaction potential duration (APD). In extended tissue, al-ternans may become spatially discordant, characterizedby out-of-phase regions in APD alternation separated bynodes where APD remains constant from beat to beat. Weinvestigate the effects that continuous and discontinousgradients ofelectrophysiological properties have on nodalformation, position and motion.

Michael BellRochester Institute of [email protected]


PP0

Coarse-Graining of Bursting Dynamics

We have developed a numerical method that maps be-tween the variables of a bursting neural network (for whichthe equations are known) and the variables of a simplifiedmodel (for which the equations are unknown). By simu-

lating the neural network for short periods of time we canestimate the dynamics the simplified model should retainand gain a better understanding of the restrictions on theparameters domain for which the simplification is valid.

Alona Ben-TalMassey UniversityInstitute of Information & Mathematical [email protected]

Ioannis KevrekidisDept. of Chemical EngineeringPrinceton [email protected]

Joshua DuleyMassey Universityjosh [email protected]

PP0

Why People Walk in Circles?

People use their senses, most dominantly sight and hear-ing, to interpret geographical cues in order to navigate toa target location. How does the process work if no cues arepresent and the only information is the initial direction to-wards the target location? Experiments suggest that peo-ple are not capable of walking straight and form surpris-ingly small looped trajectories. The analysis of experimen-tal data infers a parametric family of stochastic differencemodels with individual-based set of parameters reflectingthe directional bias and other properties of individual’s mo-tion. We analyze the stochastic process in terms of the firstexit time problem.

Katarina BodovaComenius University [email protected]

Michal JanosiComenius University, [email protected]

PP0

Use of Quasi-Steady-State Assumptions in theAnalysis of Biophysical Models

Many biological systems have the property that some pro-cesses evolve much faster than others. Mathematical mod-els of such systems often possess different time scales.A common first step in the analysis of these models isto remove fast variables by making quasi-steady-state as-sumptions. Unfortunately, quasi-steady-state reductioncan sometimes cause significant changes in dynamics. Wediscuss progress on establishing conditions under whichquasi-steady-state reduction is mathematically justifiableand will not disrupt the dynamics of the model.

Sebastian D. BoieUniversity of [email protected]

James SneydUniversity of AucklandDepartment of [email protected]

Vivien Kirk

DS13 Abstracts 227


PP0

Entrainment of Neuronal Models in Noise

We study properties of entrainment of stochastic neuronalmodels to periodically-modulated inputs. We considerspike phases as generated by a Markov chains on the circle,and analyze path-wise dynamic properties, such as stochas-tic periodicity (or phase-locking) and stochastic quasiperi-odicity. We show how these properties are read off of thegeometry of the spectrum of the transition operator in rep-resentative model examples, and investigate how the en-trainment properties change with parameters.

Alla BorisyukUniversity of UtahDept of [email protected]

PP0

Calcium Dynamics in Airway Smooth Muscle Cells

Free cytoplasmic calcium ions in human airway smoothmuscle cells are quite important in regulating the airwaycontraction that contributes to our normal breath. Ex-periments show in the present of agonist calcium changesin form of oscillations and propagates in waves.Here weconstruct a dynamical model to explore what leads to theoscillatory behavior, which is a way to understand how thecalcium affects our breath and will be very useful to theresearch of pathology of asthma.

Pengxing CaoMaths department of the University of [email protected]

PP0

Bifurcations in Bifurcations: a Dynamical Analysisof An Impacting T-Junction Flow

Fluid flows through pipe T-junctions appear commonly,for instance, in industrial systems and blood vessels. Weconsider a junction with square cross-section, where fluidsplits to two side channels. A local bifurcation analysis—using numerical continuation on the Reynolds numberRe—reveals a supercritical pitchfork bifurcation at Re ≈430, beyond which the outflow pipes contain asymmetriccounter-rotating vortices. A supercritical Hopf bifurcationnext occurs at Re ≈ 540.

Kevin K. ChenPrinceton [email protected]


Howard A. StoneMechanical and Aerospace EngineeringPrinceton [email protected]

Stefan RadlGraz University of Technology

[email protected]

Daniele VigoloPrinceton [email protected]

PP0

Regulation of Electrical Bursting in a Spatio-Temporal Model of a Gnrh Neuron

Gonadotropin-releasing hormone (GnRH) neurons are hy-pothalamic neurons that control the pulsatile release ofGnRH that governs fertility and reproduction in mammals.The mechanisms underlying the pulsatile release of GnRHare not well understood. We construct a spatio-temporalmodel to understand how the soma and dendrite of theGnRH neuron interact to control bursting, which is initi-ated in a region approximately 100 micrometers away fromthe soma, but is controlled by the mechanisms in the soma.

Xingjiang ChenDepartment of Mathematics, The University of [email protected]

PP0

Acoustic Detection and Ranging Using SolvableChaos

Acoustic experiments demonstrate a novel approach to de-tection and ranging that exploits the properties of a solv-able chaotic oscillator. This nonlinear oscillator includes anordinary differential equation and a discrete switching con-dition and provides the wideband transmitted waveform.The hybrid system admits an exact analytic solution asthe linear convolution of binary symbols and a single basisfunction, which enables coherent reception using a simpleanalog matched filter and without need for digital samplingor signal processing. An audio frequency implementationof the transmitter and receiver is described, and successfulacoustic detection and ranging measurements demonstratethe viability of the approach.

Ned J. CorronU.S. Army [email protected]

Mark StahlNASA Marshall Space Flight [email protected]

Jonathan N. BlakelyUS Army [email protected]

PP0

The Lorenz System Near the Loss of the FoliationCondition

We study the Lorenz system in a parameter regime wherethe foliation condition fails, which means the reduction to aone-dimensional map is not possible. We consider a tran-sition where the one-dimensional stable manifolds of twosecondary equilibria undergo a sudden dramatic change.We explain the effect of this change on the two-dimensionalstable manifold of the origin and its role in the loss of thefoliation condition.

Jennifer Creaser

228 DS13 Abstracts



PP0

Symmetry Breaking in Colliding Disk Systems

We develop an alternative collision rule to those developedin current work on hard disk systems (Dellago, Posch, et.al). The proposed collision rule leads to symmetry break-ing and the invalidation of the conjugate pairing rule forLyapunov exponents. Comparison of numerical results tothose obtained using existing methods is discussed. Theapproach is considered as one way of taming chaos in prob-lems of interacting systems with a high number of degreesof freedom.

Joseph DiniusUniversity of ArizonaProgram in Applied [email protected]

Joceline LegaUniversity of Arizona, [email protected]

PP0

Spatially-Shifted Feedback Control of TurbulentBehavior in Advection Diffusion Systems

We present experimental and theoretical results related tothe control of actively mode-locked lasers, using delayedfeedback, a problem that is equivalent to the control ofadvection-diffusion systems with spatially shifted feedback.Tiny feedback levels (1e-8 in our experiment) lead to spec-tacular efficiencies, although the process is different fromOGY-type control. This method is efficient when largetransient growth is present in the system.

Christophe Szwaj, Clement EvainLab. PhLAM, Univ. Lille1 (France)[email protected],[email protected]

Serge BielawskiPhLAM/Universite Lille I,[email protected]

Masahito HosakaNagoya University, Nagoya, [email protected]

Akira MochihashiJASRI/SPring-8, [email protected]

Masahiro KatohUVSOR, IMS (Japan)[email protected]

Marie-Emmanuell CouprieSynchrotron SOLEIL, [email protected]

PP0

Happiness and Movement on Twitter

Using status updates collected from Twitter’s gardenhosefeed, we explore population-level happiness. We employa simple real time hedonometer that is effective on largequantities of text. Many Twitter users enable geo-locationof their tweets. For these users, we explore the relationshipbetween their location, average movement, and happiness.

Morgan R. FrankUniversity of Vermont, Complex Systems [email protected]



PP0

Random and Regular Dynamics of StochasticallyDriven Neuronal Networks

Dynamical properties of Integrate-and-Fire neuronal net-works with multiple time scales of excitatory and in-hibitory neuronal conductances driven by random Pois-son trains of external spikes will be discussed. Both theasynchronous regime in which the network spikes arrive atcompletely random times and the synchronous regime inwhich network spikes arrive within periodically repeating,well-separated time periods, even though individual neu-rons spike randomly will be presented.

Pamela B. FullerRensselaer Polytechnic [email protected]

PP0

Formation of Localized Hot Spots of Criminal Ac-tivity in a Model Incorporating Non-Local Effects

A ubiquitous feature of crime is the spatially and tempo-rally patterned hot spot or local region of high levels ofcriminal activity. Understanding the dynamics and mech-anisms underlying the formation and dissipation of hotspots is of importance in modern policing. We analyzea spatially structured model of criminal activity that in-corporates non-local interactions in the environment. Wedemonstrate conditions for the formation and stability ofhot spots in a partial differential integral model.

Evan HaskellDivision of Math Science and TechnologyNova Southeastern [email protected]

Dean GardnerDivsion of Math, Science, and TechnologyNova Southeastern [email protected]

DS13 Abstracts 229

PP0

Stochastic Simulation of RNAP Elongation

Motion of a polymerase in a transcription process experi-ences multiple short pauses, which, together with high den-sity of transcribing polymerases, may effect overall tran-scription rate. We developed a new algorithm to simulateone-dimensional Total Asymmetric Simple Exclusion Pro-cess (TASEP) with open boundaries where the hoppingrates between neighboring sites are allowed to change bothin space and time. Our implementation uses multiple runsof a discrete event simulator with each run having a timecomplexity O(mn log n) where m is the total number ofsimulated polymerases and n is the length of the DNAstrand. We compare our algorithm to a classical algorithmof Boortz and Lebowitz which is being used for simula-tions of stationary distribution for TASEP with hoppingrates that depend on space only.

Jakub GedeonMontana State [email protected]


PP0

Traveling Waves in a Gasless Combustion Modelwith Heat Loss

We consider a model of gasless combustion with heat loss,where the heat loss from the system to the environment isformulated according to Newtons law of cooling. The pdesystem that describes evolution of the temperature andremaining fuel contains two small parameters, a diffusioncoefficient for the fuel and a heat loss parameter. We usegeometric singular perturbation theory to show existence oftraveling waves in this system and then study their spectraland nonlinear stability.

Anna GhazaryanDepartment of MathematicsMiami University and University of [email protected]

Stephen SchecterNorth Carolina State UniversityDepartment of [email protected]

Peter L. SimonInstitute of MathematicsEotvos Lorand [email protected]

PP0

Bifurcation Analysis of a Civil Transport Aircraft’sUpset Behaviour

Unintended and/or extreme dynamics outside the designflight envelope of an aircraft are referred to as upset be-haviour. An upset can induce a loss-of-control accident —the leading cause of civil aviation fatalities — if the pi-lot does not respond correctly. We present a bifurcationanalysis of the NASA generic airliner model that identi-fies attractors that correspond to various upset behaviour,

including different types of spin.

Stephen J. GillUniversity of [email protected]



Simon NeildDept. of Mechanical EngineeringUniversity of [email protected]

Guilhem PuyouAirbus in [email protected]

Etienne CoetzeeAirbus in the [email protected]

PP0

Approximate Deconvolution for Large-eddy Simu-lation (LES) on Adaptive Grids

LES and adaptive grids reduce the computational cost ofturbulence modeling, but combining these techniques gen-erates errors. Inaccuracies in subfilter models limit LES so-lution reliability at the grid scale, contaminating the inter-polated solution at grid interfaces. The grid interface alsoreflects high wavenumber solution components. Approx-imate deconvolution can improve the grid scale solution.Results from isotropic turbulence advected past a grid in-terface show approximate deconvolution reduces interfaceperturbations and hastens convergence to the downstreamsolution.

Lauren GoodfriendUC [email protected]

Fotini K. ChowUniversity of California, [email protected]

Marcos Vanella, Elias BalarasGeorge Washington [email protected], [email protected]

PP0

Interplay Between Energy-Market Dynamics andPhysical Stability of a Smart Power Grid

A smart power grid is currently being envisioned for thefuture in which, among other features, users would be ableto play the dual role of consumers as well as producersand traders of energy, thanks to emerging renewable energyproduction and energy storage technologies. As a complexdynamical system, any power grid is subject to physicalinstabilities. With existing grids, such instabilities tend to

230 DS13 Abstracts

be caused by natural disasters, human errors, or weather-related peaks in energy demand. We analyze the impact,upon the stability of a smart grid, of the energy-marketdynamics arising from users ability to buy from and sellenergy to other users. The stability analysis of the re-sulting dynamical system is performed assuming differentproposed models for this market of the future, and the cor-responding stability regions in parameter space are identi-fied. We test our theoretical findings by comparing themwith data collected from some existing prototype systems.

Jeffrey R. GordonUniversity of New [email protected]

Francesco SorrentinoUniversity of New MexicoDepartment of Mechanical [email protected]

Andrea MamolliUniversity of New [email protected]

Sergio PicozziUniversity of [email protected]

PP0

Using the Ensemble Kalman Filter to Track Linksin Neuronal Networks

We demonstrate the use of the unscented Kalman filterfor the detection and tracking of network links using timeseries data generated from a network of Hindmarsh-Roseneurons. We show the ability of the filter to identify thelinks when confronted with increasing amounts of noise aswell as model error. Additionally, the filter is shown to havethe ability to track non-stationary connections even whenan incorrect assumption of their dynamics is assumed.

Franz HamiltonGeorge Mason [email protected]

PP0

Shock-Fronted Travelling Wave Solutions Arisingin a Model of Tumour Invasion

Within mathematical biology there exists a class ofadvection-reaction-diffusion (ARD) models that supporttravelling wave solutions and demonstrate a possible tran-sition from smooth to shock-fronted waves. We present re-sults for one particular ARD model describing malignanttumour invasion. Numerical solutions indicate that bothsmooth and shock-fronted travelling wave solutions existfor this model. We verify the existence of these solutionsusing techniques from geometric singular perturbation andcanard theory and provide results on stability.

Kristen HarleyQueensland University of [email protected]

Graeme PettetQueensland University of TechnologySchool of Mathematical [email protected]

Peter van HeijsterDepartment of Mathematics and StatisticsBoston [email protected]

PP0

Observability of Nonlinear Dynamics of ElasticFlight Vehicle

In this paper, global observability analysis of nonlineardynamics of a flexible supersonic flight vehicle based onrank condition method is presented. The observabilityalgorithm under the input action is clarified and imple-mented. Singular value variations of flight vehicles observ-ability space is used as a criteria expressed applicable defi-nition for mathematical concept of observability in criticalregions where singular values are near to zero. Mathe-matical relations between different types of observabilityfor nonlinear dynamics is studied. Using SOSTOOLS andYalmip, a novel method is presented to find continuousobservable regions of variables. The average of conditionnumbers for observability space constructed at operationalpoints of flight system states, is compared in rigid and elas-tic models of flight vehicles to exhibit the aeroelasticity ef-fect on the observability of flight vehicle. Singular pointscreated when dimension of observability space is reduced.An Algabraic nonlinear equation set is offered to find alllocal singular points of nonlinear dynamics.

Hossein HashemiAmirkabir University of Technology(AUT-Tehranpolytechnic)[email protected]

PP0

Delay Induced Dynamics of Adaptive EpidemicModels

An extension of an epidemiological susceptible-infected-susceptible (SIS) model on an adaptive network, featuringconstant sojourn times in the infected state is investigated.Moment expansion, pair approximation and survival anal-ysis are applied for mapping the high dimensional discretemodel based on local rules onto a set of continuous macro-scopic observables. The resulting nonlinear delay differen-tial equations capturing the emergent level behavior of themodel are analyzed; revealing complex dynamical behaviorsuch as bistability, oscillations and bursting.

Cathleen HeilTechnical University DresdenInstitute of Scientific [email protected]


Thilo GrossDepartment of Chemical EngineeringPrinceton [email protected]

PP0

Analysis of Size Structured Population Models in

DS13 Abstracts 231

Marine Ecosystems

We investigate size structured population models to de-scribe specific aspects of marine ecosystems. The evolutionof the density size distribution of a population as functionof time and individual size is described by an integro-PDE.The biological questions which motivate our mathematicalinvestigations are predator-prey cycles and coexistence ofseveral species depending on e.g. resource level. We deter-mine regions in parameter space with different qualitativebehavior of the solution and present their biological inter-pretation.

Irene Heilmann, Jens StarkeTechnical University of DenmarkDepartment of [email protected], [email protected]

Ken Andersen, Uffe ThygesenTechnical University of DenmarkNational Institute of Aquatic [email protected], [email protected]

Mads Peter SørensenTechnical University of DenmarkDepartment of [email protected]

Thomas LorenzGoethe University [email protected]

PP0

Characterization and Observations of NonlinearCharged Particle Dynamics and Chaos in the Mag-netotail

The use of nonlinear dynamics modeling and satellite mea-surements of an ion distribution function signature is usedto infer the meso-scale structure of the magnetotail. Addi-tionally, we discuss quantitative measurements of particlechaos in the magnetotail focusing on the Lyapunov expo-nent and the fractal structure of the basin boundary be-tween forward and back-scattered particles. The resonancephenomena that produces the ion signature is also apparentin the Lyapunov exponent and the fractal dimensionality.

Daniel L. HollandIllinois State UniversityDepartment of [email protected]

Richard MartinIllinois State [email protected]

Hiroshi MatsuokaIllinois State UniversityDepartment of [email protected]

PP0

Effects of Freeplay on the Dynamic Stability of AnAircraft Main Landing Gear

We study the occurrence of (unwanted) shimmy oscillationsof a dual-wheel aircraft main landing gear, which is mod-elled with torsional, lateral, longitidunal and axial degrees

of freedom, as well as freeplay in the torque-link. By meansof a bifurcation study in dependence on forward velocityand loading force on the gear, we show that the occurenceor not of shimmy oscillations depends very sensitively onthe amount of freeplay.

Chris HowcroftUniversity of [email protected]




Duncan PattrickAirbus in the [email protected]

PP0

Computing Stability of Mosquito Motion

We use the rigid body simulation software TREP to createa computational model of a mosquito. Using quasi-steadyassumptions for the wing aerodynamics, along with an im-posed periodic wing motion drawn from measurements ofmosquitoes, we perturb the wing motion and body initialconditions to find steadily translating states of the insect’sbody motion. We then examine the stability characteris-tics of these states, finding pitch and roll instabilities, alongwith a non-self adjoint structure to the Jacobian matrix.

Sarah IamsUniversity of CambridgeCambridge, [email protected]

PP0

Synchronization of Hypernetworks: Dimension-ality Reduction Through Simultaneous Block-Diagonalization of Matrices

We present a general framework to study stability of thesynchronous solution for a hypernetwork of coupled dy-namical systems. We are able to reduce the dimensionalityof the problem by using simultaneous block-diagonalizationof matrices. Under certain conditions, this technique mayyield a substantial reduction of the dimensionality of verylarge systems. We apply our reduction technique to a num-ber of different examples.

Daniel IrvingUniversity of New MexicoMecanical Engineering [email protected]

Francesco SorrentinoUniversity of New Mexico

232 DS13 Abstracts

Department of Mechanical [email protected]

PP0

2-θ Neuron Model for 3-Cell Inhibitory CentralPattern Generators

We examine bifurcations and stability of multi-patterns in3-cell CPGs of inhibitory bursting neurons using 2-θ neu-ron models. Reducing the Hodgkin-Huxley models to 1D2-θ models allows comprehensive analysis of the system.The model was tested for the transitions to specific robustbursting patterns as found in plausible Hodgkin-Huxleymodels and follow pattern formations with duty-cycle andasymmetric connections. Pattern detection and stabilityare determined using return maps for phase-lags on 2Dtori.

Aaron [email protected]


Joesph [email protected]

PP0

Interaction Between Aircraft Landing Gear Dy-namics and Fuselage Modes

Cockpit vibrations experienced by pilots during aircrafttake off and landing are thought to be caused by shimmyoscillations of the nose landing gear that feed into the fuse-lage. To test this hypothesis and to investigate the natureof the mutual interaction involved, a mathematical modelis presented that couples the nose landing gear dynamicswith horizontal and vertical modes of the fuselage.

Sarah E. KewleyUniversity of [email protected]




Thomas Wilson, Robert [email protected], [email protected]

PP0

Distributive Zooplankton Digestion Delay onPlanktonic Dynamic

A mathematical model is proposed to study of the dis-tributive zooplankton digestion delay on planktonic dy-namic. The model includes three state variables viz., nutri-ent concentration, phytoplankton biomass and zooplank-ton biomass. The release of toxic substance by phyto-plankton species reduces the growth of zooplankton andthis plays an important role in plankton dynamics. In thispaper, we introduce a delay (time-lag) in the digestion ofphytoplankton by zooplankton. The stability analysis ofall the feasible equilibria are studied and the existence ofHopf-bifurcation for the interior equilibrium of the systemis explored. From the above analysis, we observe that thesupply rate of nutrient and delay parameter play importantrole in changing the dynamical behaviour of the underly-ing system. Further we have derived the explicit algorithmwhich determine the direction and the stability of Hopf-bifurcation solution. Finally numerical simulation is car-ried out to support the theoretical result.

Swati KhareHindustan College of Science & Technology, [email protected]

PP0

A Closed Npz Model With Delayed Nutrient Re-cycling

We consider a closed Nutrient-Phytoplankton-Zooplankton(NPZ) model that allows for a delay in the nutrient re-cycling. Mathematical properties that come from such amodel are discussed, as well as their biological implications.Biomass is conserved in the system in a way that relates tothe delay distribution of the nutrient recycling. The sta-bility of the equilibrium solutions depends on the quantityof biomass in the system as well as on the length of delay.

Matt KloostermanUniversity of [email protected]

Sue Ann CampbellUniversity of WaterlooDept of Applied [email protected]

Francis PoulinDepartment of Applied MathematicsUniversity of [email protected]

PP0

Chaos and Reliability in Fluctuation-Driven, Bal-anced Spiking Networks

The question of reliability arises for any dynamical systemdriven by an input signal: if the same signal is presentedmany times with different initial conditions, will the systementrain to the signal in a repeatable way? Reliability is ofparticular interest in large, randomly coupled networks ofexcitatory and inhibitory units. Such networks are ubiq-uitous in neuroscience, but are known to autonomouslyproduce strongly chaotic dynamics an obvious threat toreliability. Here, we show that such chaos also occurs inthe presence of weak and strong stimuli. However, even inthe chaotic regime, intermittent periods of highly reliable

DS13 Abstracts 233

spiking often coexist with unreliable activity. We propose aframework to better understand these complex dynamics,leveraging results from random dynamical systems (RDS)theory, by establishing the effect of the underlying chaoticattractor’s geometry on output spike trains.

Guillaume LajoieDepartment of Applied MathematicsUniversity of [email protected]

Kevin K. LinUniversity of [email protected]


PP0

Isochrons in the Fitzhugh-Nagumo Model

An isochron is the set of all points in the basin of an attract-ing periodic orbit that converge to the periodic orbit withthe same asymptotic phase. We will demonstrate how, viathe continuation of suitable orbit segments, isochrons canbe computed accurately and reliably. As a concrete exam-ple we determine the isochrons of the Fitzhugh-Nagumomodel as studied by Arthur Winfree in 1980.

Peter LangfieldUniversity of [email protected]


PP0

Aggressive Shadowing of a Low-Dimensional Modelof Atmospheric Dynamics

Predictions of atmospheric dynamics suffer from the con-sequences of chaos: models quickly diverge from observa-tions, as initial state uncertainty is amplified by nonlinear-ity. Using the Lorenz ’96 coupled system, we extend a tech-nique called inflation, whereby the ensemble of forecastsis regularly expanded artificially along contracting dimen-sions. Targeted inflation is shown to increase the lengthof time for which the best ensemble member remains closeto the truth. Utilized appropriately, inflation may improvepredictions for the future states of physical phenomena.

Ross [email protected]


PP0

Numerical Continuation of Invariant Solutions of

Pdes with Symmetries

We consider the problem of numerically continuing solu-tions of partial differential equations (PDEs) with sym-metries. In particular, we work with the 1D complexGinzburg-Landau equation (CGLE) and will present a nu-merical study designed to continue a set of invariant solu-tions of the CGLE from one chaotic regime into another.

Vanessa Lopez-MarreroIBM T. J. Watson Research [email protected]

PP0

Asymmetric Coherent Structures in One and TwoSpace Dimensions

We consider the effects of symmetry breaking perturba-tions on localized structures in one and two space dimen-sions. In particular, we develop a general framework forunderstanding the effects of such perturbations on patternformation, construct a scenario under which isolas are pre-dicted to bifurcate from a snaking solution branch, anddemonstrate numerically that the solutions of such a sys-tem evolve as predicted.

Elizabeth J. MakridesBrown UniversityDivision of Applied Mathematicselizabeth [email protected]


PP0

Assimilation of Lagrangian Ocean Data

Lagrangian instruments which are carried by the flow havebecome popular tools for providing measurements of oceandynamics. Ocean dynamics are often modeled as nonlin-ear processes, and this nonlinearity creates a sensitivity toinitial conditions and model parameters that can ruin fore-casts even with relatively small errors in estimates of theseparameters. This work focuses on assimilating Lagrangiantracer data into nonlinear models of ocean dynamics to im-prove estimates of initial conditions and model parameters.

Adam B. MallenMarquette [email protected]

PP0

Asynchronous Inhibition and Small Neuronal Net-work Dynamics

In cortical neuronal network models, basket cells are as-sumed to mediate a fast phasic inhibitory signal throughGABA-A synapses via synchronous release of neurotrans-mitter vescicles. Recent experiments have studied a classof basket cells that release asynchronous neurotransmit-ter release. In this study we investigate the dynamics ofa small neuronal network with excitatory, fast-spiking in-hibitory and a novel class of inhibitory neurons that canrelease neurotransmistter vescicles asynchronously.

Sashi Marella

234 DS13 Abstracts

University of PittsburghCenter for [email protected]

PP0

Voltage-Dependent Stochastic Gating Models OfTric-B Channels

TRIC-A and TRIC-B are two, related, trimeric intracellu-lar cation channels present in sarcoplasmic reticulum (SR)and are thought to provide counter-current for SR Ca2+-release that is crucial for muscle contraction. We presentstochastic models of the voltage-regulated gating of TRIC-B channels based on single channel data. We analyse the ef-fects of different connectivity schemes on model behaviourin order to better evaluate and understand the role of thision channel in intracellular calcium release and control.

Antoni Matyjaszkiewicz, Elisa VenturiUniversity of [email protected],[email protected]

Daiju Yamazaki, Miyuki Nishi, Hiroshi TakeshimaKyoto [email protected],[email protected],[email protected]

Krasimira Tsaneva-AtanasovaDepartment of Engineering MathematicsUniversity of [email protected]

Rebecca SitsapesanUniversity of [email protected]

PP0

Dynamics, Networks and Energy Efficiency

Models of innovation uptake can be based on various fac-tors: a) rational decision-making with regards to the in-trinsic value of a product; b) social spreading of technologyor ideas induced by peer-to-peer communication of infor-mation; c) interaction with the “market’ via a global feed-back. For certain innovative technologies or behaviours thedecision to adopt may be based on a combination of thesefactors. This is particularly the case for energy-relatedinnovations, where some are more visible and socially de-sirable (such as solar panels) compared to others which arehidden (such as home insulation). We introduce a thresh-old diffusion model for the dynamics of the adoption of suchinnovations that is based on a combination of all three fac-tors, along with dynamical-systems inspired methods foranalysing and understanding the numerically observed dif-fusion behaviour.

Nick McCullenArchitecture and Civil EngineeringUniversity of [email protected]

Alastair M. RucklidgeDepartment of Applied MathematicsUniversity of [email protected]

Catherine BaleEnergy Research InstituteUniversity of [email protected]

Timothy FoxonSchool of Earth and EnvironmentUniversity of [email protected]

William GaleSchool of Process, Environmental and MaterialsEngineering,University of [email protected]

PP0

Optimal Control in Lagrangian Data Assimilation

Inferring the state of an ocean flow is an integral part ofenvironmental monitoring, conservation efforts, and miti-gation strategies for weather events. Autonomous vehicleswith a limited capacity for locomotion are increasingly be-ing used for data assimilation of quantities of interest inthe ocean, including the time-dependent velocity field. Weassess the efficacy of optimal control techniques to guideLagrangian data assimilation in 1- and 2-dimensional flows,focusing on assimilation of the velocity field itself.

Richard O. MooreNew Jersey Institute of [email protected]

Damon McDougallInstitute for Computational Engineering SciencesThe University of Texas at [email protected]

PP0

An Adaptive Algorithm for Estimation of SynapticStrengths in a Network of Neurons

The behavior of interconnected neurons depends largely onthe synaptic coupling and can be analyzed using nonlineardynamical models. Finding the strength of connections re-quires developing a new system identification method toovercome problems of nonsmooth error function and un-observable states. We describe an adaptive algorithm todetermine the connections in a self-oscillatory network ofIzhikevich neurons. Individual membrane potentials areobserved and the states of the model are estimated by theUnscented Kalman Filter.

Anish MitraDepartment of Electrical and Computer EngineeringGeorge Mason [email protected]

Andre ManitiusFaculty of Electrical and Computer EngineeringGeorge Mason [email protected]

PP0

Lobe Dynamics and Homoclinic Tangles in Atmo-spheric Flows

The primary concern for geophysical flows are the finite

DS13 Abstracts 235

time nature and the arbitrary time dependence in con-trast to classical dynamical systems. Recent work on2D quasi-horizontal approximations of atmospheric mo-tion have demonstrated that there are aperiodic, finite-time analogs of homoclinic tangles and lobe dynamics,e.g., around hurricane boundaries, such as using FTLEbased identification of coherent structures. We apply meth-ods based on Lagrangian descriptors (due to Mancho andco-workers) to locate distinguished hyperbolic trajectories(DHTs) and generate corresponding finite-time stable andunstable manifolds to study lobe dynamics, as applied toatmospheric flow as well as fluid experiments. We comparethe Lagrangian descriptor approach with the FTLE-basedapproach.

Shibabrat NaikEngineering Science and MechanicsVirginia [email protected]


PP0

Stability and Bifurcation Analysis of Rigid Space-craft Spin Stabilization Using Delayed FeedbackControl

The stability and bifurcation of closed loop delayed feed-back control for spin stabilization of a rigid spacecraft isinvestigated, in which intermediate axis spin is stabilized.Linear stability is analyzed via the exponential-polynomialcharacteristic equation, while the normal form of the Hopfbifurcation is analytically obtained via the method of mul-tiple scales and verified using continuation software. Theobtained stability regions and bifurcations are verified withnumerical simulations.

Eric A. ButcherNew Mexico State UniversityNew Mexico State [email protected]

Morad NazariNew Mexico State [email protected]

PP0

Bifurcations of Large Networks of Two Dimen-sional Integrate and Fire Neurons

Recently, a class of two-dimensional integrate and fire mod-els has been used to faithfully model spiking neurons. Thisposter introduces a technique to reduce a full network ofthis class of neurons to a mean field model, consisting ofa system of switching ordinary differential equations. Themean field equations are able to qualitatively and quan-titatively describe the bifurcations that the full networksdisplay. Extensions to heterogeneous networks of oscilla-tors and other applications are discussed.

Wilten NicolaUniversity of [email protected]

Sue Ann CampbellUniversity of Waterloo

Dept of Applied [email protected]

PP0

Pattern Formation in Small-world Networks

The Turing instability is a classic mechanism for the forma-tion of spatial structures in non-equilibrium systems andhas recently been investigated by Nakao and Mikhailov inthe context of complex networks. Inspired by their workwe investigate the Swift-Hohenberg equation when posedon a small-world network. We find a branch of solutionsthat snakes upward when a quintic term is included, justas in the PDE setting.

Jitse NiesenUniversity of [email protected]

PP0

Rigorous Numerical Verification of Uniqueness andSmoothness in a Surface Growth Model

We study three different methods, based on numerical dataand a-posteriori analysis, to verify rigorously the unique-ness and smoothness of global solutions. The methods areapplied to a scalar surface growth model and compared nu-merically. Despite of being scalar, this model is similar to3D-Navier Stokes and serves as a toy problem.

Christian NoldeUniversitat [email protected]


James RobinsonUniversity of [email protected]

PP0

Sleep-Wake Transition Dynamics

Regulation of sleep-wake transitions presents a uniquemathematical challenge in understanding sleep. Competi-tive interactions between two mutually inhibitory neuronalnetworks are involved in these transitions and it is knownthat wake bout durations follow a power-law distributionin several species. Here we explore the role of networkarchitecture in generating sleep-wake transitions and de-velop a statistical tool to analyze simulated distributionsof activity bouts.

Fatih Olmez, Janet Best, Jung Eun KimThe Ohio State [email protected], [email protected],[email protected]


Peter R. KramerRensselaer Polytechnic InstituteDepartment of Mathematical Sciences

236 DS13 Abstracts

[email protected]

John [email protected]

PP0

Bifurcations and Rhythms in a Mutually InhibitoryThree-Neuron Network

Inhibitory neuronal networks arise throughout the cen-tral nervous system and play an important role in rhythmgeneration. It is thus crucial to understand the mecha-nisms underlying the dynamics of these networks and howfeedback signals from physiological components modulatetheir outputs. We consider a mutually inhibitory three-neuron network and analyze how intrinsic dynamic fea-tures, synaptic connections, and various inputs interact toaffect complex bifurcation structures of the network andthereby modulate network outputs.

Choongseok ParkDepartment of MathematicsUniversity of [email protected]

Jonathan RubinUniversity of PittsburghPittsburgh, [email protected]

PP0

Saturated Perturbation in Pyragas MethodsThrough Nonlinear Feedback Control

Using time-continuous control for controlling chaos wasstated by Pyragas. He introduced the proportional anddelayed feedback control methods. He modified them by asaturated perturbation based on a piecewise linear controllaw to avoid large perturbations and multistability. Wepropose an alternative nonlinear bounded element into thefeedback law. Local convergence is shown while the desiredsaturation of the perturbation is assured. Different aspectsof our proposal are analyzed and confronted with Pyragasmethods.

Veronica E. Pastor, Graciela GonzalezFaculty of EngineeringUniversity of Buenos [email protected], [email protected]

PP0

Prey Switching with a Linear Preference Trade-off

We study piecewise-smooth models of predator-prey inter-action to describe predator’s adaptive change of diet. Weshow that a 1 predator-2 prey system with a tilted switch-ing manifold between the discontinuous vector fields goesthrough a Hopf-like bifurcation, followed by an adding-sliding bifurcation, and period doubling. Our model simu-lations capture the periodicity in the ratio between preda-tor’s preferred and alternative prey types exhibited by dataon freshwater plankton.

Sofia Piltz, Mason A. PorterUniversity of [email protected], [email protected]

Philip K. MainiOxford University, Mathematical Inst. 24-29 St. GilesOxford. OX1 [email protected]

PP0

Global Dynamics of the Subcritical Hopf NormalForm Subject to Pyragas Time-Delayed FeedbackControl

Pyragas time-delayed feedback control is designed to sta-bilize an unstable periodic orbit, such as the one in thewidely used normal form of a subcritical Hopf bifurcation.Previous work focused primarily on the mechanism of sta-bilization. Here we present a global picture of the dynam-ics induced by the time-delayed feedback. In particular,we consider how infinitely many delay-induced Hopf bifur-cation curves move as the 2π-periodic feedback phase isvaried.

Anup S. Purewal, Claire PostlethwaiteUniversity of [email protected],[email protected]


PP0

A New Phase Space Method for Radar/acousticTarget Discrimination

We have developed a method for target discrimination em-ploying chaos based waveforms and a nearest neighborstrand separation metric. Chaotic rf FDTD simulation oracoustic experimental waveform data reflected from sev-eral similar targets were embedded and nearest neighborstrands were identified. We distinguish between targets bychoosing between optimized known strand configurationsthat minimize the average strand separation of unknownscattered waveforms. The method is robust in the pres-ence of substantial noise and clutter.

Frederic J. RachfordNaval Reserach LaboratoryMaterial [email protected]

Thomas CarrollNaval Research LaboratoryMaterial [email protected]

PP0

Localised States and Pattern Formation in a NeuralField Model of the Primary Visual Cortex

The primary visual cortex has been shown to maintain lo-calised patterns of activity when oriented stimuli are pre-sented in the visual field. For specific choices of the con-nectivity function defining intra-cortical connections it ispossible to derive a PDE reduction that allows for stan-dard dynamical systems tools to be applied. We computeand path follow both radially-symmetric bump solutionsand non-radially-symmetric patterns with D6 symmetry;

DS13 Abstracts 237

these solutions are linked to experimental observations.

James RankinINRIA [email protected]

David LloydUniversity of [email protected]

Gregory FayeSchool of MathematicsUniversity of [email protected]

Frederic ChavaneCNRSInstitut de Neurosciences de la [email protected]

PP0

Mining Experimental Data from the Chaotic Wa-terwheel

A large collection of experimental data of the motion ofa Malkus-Lorenz waterwheel is analyzed. Progress will bereported on a number of fronts: application of Gottwalds0-1 test for chaos to the data; determining fixed point loca-tion from phase space trajectories; extracting the motionof the waters center of mass location from the time seriesdata; and determining the variation of total water mass inthe wheel (generally assumed constant) via dynamic forcemeasurements.

George RutherfordDepartment of PhysicsIllinois State [email protected]

Richard MartinIllinois State [email protected]

PP0

Dynamics of An Seqihrs Epidemic Model with Me-dia Awareness, Quarantine, Isolation and Cross-Protective-Immunity

An autonomous deterministic non-linear epidemic modelSEQIHRS is proposed for the transmission dynamics of ahighly contagious disease with quarantine, isolation andcross-protective-immunity. The DFE is GAS for R0 < 1and forR0 > 1 the unique endemic equilibrium is LAS. Theimpact of non-pharmaceutical prophylaxis through mediaawareness is assessed and estimated through a new ap-proach. It is observed that if the level of transmission byisolated individuals in hospitals is high enough, then theuse of quarantine and isolation could offer a detrimentalpopulation-level impact.

Govind P. SahuABV Indian Institute of Information Technology& Management Gwalior, [email protected]

Joydip DharABV Indian Institute of Information Technology &Management

Gwalior, [email protected]

PP0

Delayed Feedback Attitude Stabilization of RigidBody Motion on So(3) Via Liapunov-KrasovskiiFunctionals

This paper addresses the stabilization problem of rigidbody motion on SO(3) in presence of an unknown con-stant time delay in the measurements. By employing aLyapunov-Krasovskii functional, a delay dependent stabil-ity condition is obtained in terms of a linear matrix in-equality, which results in linear control gain matrices. Inaddition, an estimate of the region of attraction of the sys-tem is obtained. A set of simulations are performed andcompared with previous works.

Ehsan SamieiNew Mexico Sate [email protected]

Maziar Izadi, Amit SanyalNew Mexico State [email protected], [email protected]

Eric A. ButcherNew Mexico State UniversityNew Mexico State [email protected]

PP0

An Agent-Based Model for Stripe Formation in Ze-bra Fish

Zebra fish develop stripe patterns composed of pigmentedcells during their early development. Experimental workby Kondo and his collaborators has shed much light onhow stripes form and how they are regenerated when pig-mented cells are removed. Theoretical work has focusedon reaction-diffusion models. Here, we use an agent-basedmodel for cell birth and movement to gain further insightinto the processes and scales involved in stripe formationand regeneration.

Bjorn Sandstede, Alexandria VolkeningBrown Universitybjorn [email protected],alexandria [email protected]

PP0

Use of Optogenetics for Control of CorticalSeizures

The use of charge balanced feedback control for thesuppression of seizure like activity has been successfullydemonstrated in one and two dimensional cortical models.The controller works through control of bifurcations. Ex-tending this, we study the bifurcations produced by chargebalanced optogenetic control in a two dimensional corticalmodel by the optical stimulation of neurons, and its effecton the non-linear dynamics of seizures.

Prashanth Selvaraj, Andrew SzeriUniversity of California, [email protected], [email protected]

238 DS13 Abstracts

PP0

Modeling of Chaotic Time Series Using ChamferDistance

We tried to make a mathematical model of low dimensionalchaos by using Chamfer distance which is used in computervision.

Masanori ShiroNational Institute of Advanced Industrial Science [email protected]

PP0

Dynamics of Vegetation Patterns under SlowlyVarying Conditions

We consider an extension of the Klausmeier model forvegetation patterns, that incorporates nonlinear diffusion.With continuation software an overview of coexistent sta-ble steady states can be constructed: the Busse balloon. Itis found that patterns exhibited by the model repeatedlysuffer from abrupt decreases in wavenumber ultimatelyleading to desert, as a parameter decreases. It will beshown that these abrupt changes correspond directly tointeractions with the boundary of the Busse balloon.

Eric SieroLeiden University, Mathematical [email protected]

Jens RademacherCWI, Amsterdam, [email protected]


PP0

Amplitude Equations for a Period-Doubling Bifur-cation in a Neural-Field Model

We examine a two population neural-field model with tem-poral periodic forcing and a piecewise linear firing rate. Weperform computer simulations and observe a period dou-bling bifurcation with non-zero wave-number. We then usethe piecewise linear nature of the firing rate to constructanalytically the underlying spatially homogeneous periodicorbit. Performing linear stability analysis allows us to pre-dict the position of the bifurcation. Finally we formulatethe amplitude equations for this model.

Ruth M. SmithUniversity of [email protected]

PP0

Multiple Rhythms from One Network: PhasePlane Analysis of Rhythmic Activity in Turtle Mo-tor Circuits

We analyze a proposed central pattern generators abilityto produce differing motor patterns from a single pool ofneurons under different tonic drives. A key issue is a par-ticular motoneurons response to different phasic synapticinputs. We study the impact of these phasic inputs onmotoneuron phase space and on properties of associated

trajectories and show how these yield sufficient conditionsfor reproduction of observed rhythms. A contraction argu-ment leads to existence of a stable solution.

Abigail SnyderUniversity of [email protected]

Jonathan RubinUniversity of PittsburghPittsburgh, [email protected]

PP0

Investigating Network Structure in LocomotorModels

Central pattern generators (CPGs) are neuronal networksthat produce rhythmic activity in the absence of bothrhythmic input and afferent feedback. These networks un-derlie various rhythmic animal movements, such as locomo-tion. We propose and analyze CPG networks that are ableto replicate particular locomotor patterns. This extendsprevious modeling efforts by providing a more detailed de-scription of the contribution of intrinsic neuronal dynam-ics and network structure to the mechanisms underlyingrhythm generation in locomotion.

Lucy SpardyMathematical Biosciences [email protected]

PP0

Growth of Diffusion Limited Aggregation (DLA)-Grass like branched pattern via Turing pattern for-mation in a Belousov-Zhabotinskii (B-Z) type re-action system

Nanostructured growth DLA-Grass like branched patternin a B-Z type reaction system by using ethyl acetoacetate-adipic acid as a duel organic substrate has been reported.The system in liquid phase has been found to show Turingtype pattern. The solid phase nucleation has been foundto occur in the colloidal phase (composed of nano size par-ticles) and has been found to grow in symmetric crystalpattern with the progress of the reaction finally exhibitDLA morphology.

Rohit Srivastava, Prem Kumar SrivastavaBirla Institute of Technology Deoghar Campus-814142,[email protected], [email protected]

PP0

Return Times and Rates of Fluid Mixing

Research in smooth ergodic theory is delivering results onrates of mixing in abstract dynamical systems. We reporton the relevance of such results to fluid mixing problems.

Rob SturmanUniversity of [email protected]

PP0

Stochastic Endemic Sir Model and Its Properties

We consider the stochastic endemic SIR model. This is a

DS13 Abstracts 239

generalization of the classic endemic SIR model in whichthe coefficients depend on a semi-Markov process describ-ing a random media. Under stationary conditions of thesemi-Markov media we study an averaging and diffusionprinciples for the perturbed stochastic endemic SIR model.In the case of avereging principle we get classic endemic SIRmodel with averaged coefficients, and in the case of diffu-sion approximation we obtain the diffusion endemic SIRmodel. We also study stability properties of the stochasticendemic SIR model.

Mariya Y. SvishchukMount Royal [email protected]

PP0

Performance Evaluation of Indoor Power LineCommunication Using Chaos CDMA

Power line communication is a technology that is usedfor data transmission on electric power lines. Becauseimpedance mismatching and branched lines cause signalreflections, power line channels possess multi-pass fadingcharacteristics. In this study, the performance of a syn-chronous code division multiple access (CDMA) using thechaotic spreading sequences with constant power is esti-mated in indoor power line channels.

Ryo TakahashiDepartment of Electrical Engineering,Graduate School of Engineering, Kyoto [email protected]

Ken UmenoDepartment of Applied Mathematics and PhysicsGraduate School of Informatics, Kyoto [email protected]

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Coupled Aircraft Nose Landing Gear and FuselageDynamics

Under certain conditions during take-off and landing, pi-lots may experience sometimes quite strong vibrations inthe cockpit. We present a mathematical model for a cou-pled aircraft nose landing gear and fuselage system. Abifurcation analysis reveals that self-sustained shimmy os-cillations of the landing gear can trigger considerable fuse-lage dynamics. The system behaviour depends strongly onthe modal characteristics of the fuselage.

Nandor TerkovicsUniversity of [email protected]




Sanjiv Sharma, Peter [email protected], [email protected]

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A Discontinuous Galerkin Method for ModelingTranscription

A Discontinuous Galerkin Finite Element Method is usedfor the simulation of a nonlinear conservation law PDEwhich models traffic flow with several traffic lights. Thisis used to model the motion of polymerases on ribosomalRNA. Physically relevant pauses are incorporated into themodel. These pauses result in delays during the transcrip-tion process, possibly affecting protein production. Usingthe DG solution, the average delay experienced by a poly-merase is estimated.

Jennifer Thorenson, Lisa G. DavisMontana State [email protected], [email protected]


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Linear Frequency Response Theory for Au-tonomous, Chaotic Oscillators

We propose to define a linear frequency response func-tion for autonomous, structurally stable chaotic oscillators,which measures the change of the average frequency un-der a stationary perturbation. We furthermore link thisfrequency response function to the field of zero Lyapunovvectors and discuss the applications and limitations of thisapproach.

Ralf ToenjesOchanomizu University,Ochadai Academic [email protected]

Hiroshi KoriDivision of Advanced SciencesOchanomizu [email protected]

Kazumasa TakeuchiThe University of [email protected]

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Empirically Determined Adjoint Operators for theCoarse Control of Distributed Microscopic Pro-cesses

We present a method for the design of coarse-grainedlinear controllers for spatially distributed processes in amulti-scale, “equation-free’ computational environment.This method is applied to two prototypical problems:a black-box linearized Ginzburg-Landau simulator and aFitzHugh-Nagumo simulator based on Lattice-Boltzmannmethods. In both cases, short bursts of the full simulationare used to locate the steady state and approximate theadjoint of the Jacobian well enough for an effective coarse

240 DS13 Abstracts

controller to be designed.

Matthew O. WilliamsApplied MathematicsUniversity of [email protected]

Ioannis KevrekidisDept. of Chemical EngineeringPrinceton [email protected]


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Kneading Invariants for the Elucidation of Chaos

A computational technique based on the symbolic descrip-tion utilizing kneading invariants is proposed for the ex-ploration of parametric chaos in systems with the Lorenzattractor. The technique elucidates the stunning complex-ity and universality of the patterns discovered in the bi-parametric scans of given models and detects their orga-nizing centers codimension-two T-points and separatingsaddles.

Jeremy WojcikGeorgia State UniversityDept. Mathematics and [email protected]

Tingli XingGeorgia State [email protected]



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