Dynamic ModelsLecture 13

Dynamic Models: IntroductionDynamic models can describe how variables change over time or explain variation by appealing to mechanisms.The informatics systems described in this lecture focus on explanatory models derived from scientific knowledge. There are several approaches to dynamic modeling, but we focus on systems that represent models based onAlthough not exhaustive, these approaches cover a broad range of modeling techniquesqualitative process theory,differential and algebraic equations, and agent-level behavior.

Dynamic Models: Historical UseLimits to GrowthOthers

Garp3The Garp3 environment supports qualitative process models, which emphasize processes and entities.The entities in this hierarchy have properties altered during simulation.A model is a collection of model fragments that define its dynamics.Scenarios give the starting values for the properties of entities.This scenario starts with a small number of green frogs.The model explains frog population dynamics.

Garp3: Model FragmentsThis process defines the positive population growth model fragment.The growth rate of a population directly influences its size.Additionally, population size is proportional to the growth rate.Here the growth rate is fixed to Plus, which is any positive number.This entity definition states that a population must have the property Number of.

Garp3: SimulationGiven a starting scenario, Garp3 models produce envisionments of the state space.Each state differs in its values for entity properties.These trajectories show the properties in states 3, 4, and 6.Population growth was forced to be positive.The number of frogs increases over time as one would expect.

STELLAThe STELLA environment supports system dynamics models based on Forrester diagrams.A stock accumulates quantities (e.g., fish, chemicals, people)A flow controls the movement of quantities between stocks.A converter carries out algebraic transformations of quantities.

Quantities may flow from infinite sources or to infinite sinks.

STELLA: Model Display

STELLA: Model ConstructionModel construction in STELLA involves laying out the visual components and specifying their properties.The being born flow is defined as:Population * birth fractionThe parameter birth fraction is set to 0.5, but may be tuned.

Stock:requires an initial value defined by a constant or an equation.Flow:requires an equation to transfer quantities between stocks.Converter:requires a constant or an equation to define its influence.

STELLA: Model SimulationSome of the equations from the Easter Island model.Simulated trajectories from the Easter Island model.

NetLogoThe NetLogo environment supports agent-based models, which stress individual and environmental interaction.NetLogo models are represented in a procedural language, but are controlled by custom graphical interfaces.Controls are on the left.Variable trajectories are displayed on the bottom.The environment and agents appear on the right.This model explores the social dynamics of rebellion.

NetLogo: Model Construction;; COP BEHAVIORto enforce if any? (agents-on neighborhood) with [active?] [ ;; arrest suspect let suspect one-of (agents-on neighborhood) with [active?] ask suspect [ set active? false set jail-term random max-jail-term ] move-to suspect ;; move to patch of the jailed agent ]endThis example shows the code that controls the interaction between a cop and an agent in the same region.The cop will arrest a nearby rebellious (active) agent, who will go to jail for a random amount of time.

NetLogo: SimulationThe agent window shows:jailed agents as dark circles,active agents as red circles,quiet agents as green circles, andcops as blue triangles.

NetLogo also displays trajectories for the various agent populations.

PrometheusThe Prometheus environment supports quantitative process models which emphasize variables and processes.The light availability process calculates lights limiting factor on plant growth. Death, grazing, and growth processes control the dynamics of the phytoplankton population.Phytoplankton affects grazing rate and nitrate uptake.

Prometheus: Model RepresentationThe graphical representation shows causal interactions.Corresponding differential and algebraic equations.

Prometheus: Editing and Simulating ModelsScientists can instantiate processes from a library.

Simulating models produces a trajectory for each variable.

Dynamic Models: SummaryThe informatics systems discussed in this lecture covered several modeling styles:Garp3 is unique in that it represents dynamics as discrete state transitions;STELLA treats the world as quantities of stuff that undergo constant transformation;Prometheus represents the world in terms of mechanisms that drive system evolution; andNetLogo distinctively focuses on individual interactions as opposed to aggregate entities or quantities.These different modeling paradigms reflect and influence scientific thinking about dynamical systems.

all images are screenshots from the respective applicationsadd slides on e-cell, computational physics (n-body)*