Global Attractorsin Biochemical Dynamics

Gheorghe CraciunDepartment of Mathematics and

Department of Biomolecular ChemistryUniversity of Wisconsin-Madison

Example

The Lorenz equations

Example

Example

Example

Notation:

Vector equations for mass action kinetics

Notation:

Vector equations for mass action kinetics

Notation:

Vector representation ofdifferential equations:

Vector equations for mass action kinetics

Notation:

Vector representation ofdifferential equations:

Stoichiometric Subspace

Example:

Decomposition of the reaction rate function

Decomposition of the reaction rate function

Decomposition of the reaction rate function

Decomposition of the reaction rate function

C1

C4 C 3

C2

C 5

Deficiency of a reaction network

(1)

Remark:

Remark:

(description of the kernel of A )k

Weakly reversible networks

Existence of positive fixed points