# Stability and Instability in Polynomial Equations Arising from Complex Chemical Reaction Networks: Some Underlying Mathematics

Monday, March 5, 2007 - 2:50pm - 3:40pm

EE/CS 3-180

Gheorghe Craciun (University of Wisconsin, Madison)

Chemical reaction network models give rise to

polynomial

dynamical systems that are usually high dimensional,

nonlinear, and

have many unknown parameters. Due to the presence of these

unknown

parameters (such as reaction rate constants) direct numerical

simulation of the chemical dynamics is practically

impossible. On

the other hand, we will show that important properties of

these

systems are determined only by the network structure, and do

not

depend on the unknown parameters. Also, we will show how some

of

these results can be generalized to systems of polynomial

equations

that are not necessarily derived from chemical kinetics. In

particular, we will point out connections with classical

problems

in algebraic geometry, such as the real Jacobian conjecture.

This

talk describes joint work with Martin Feinberg, and can be

regarded

as a continuation of his earlier talk.

polynomial

dynamical systems that are usually high dimensional,

nonlinear, and

have many unknown parameters. Due to the presence of these

unknown

parameters (such as reaction rate constants) direct numerical

simulation of the chemical dynamics is practically

impossible. On

the other hand, we will show that important properties of

these

systems are determined only by the network structure, and do

not

depend on the unknown parameters. Also, we will show how some

of

these results can be generalized to systems of polynomial

equations

that are not necessarily derived from chemical kinetics. In

particular, we will point out connections with classical

problems

in algebraic geometry, such as the real Jacobian conjecture.

This

talk describes joint work with Martin Feinberg, and can be

regarded

as a continuation of his earlier talk.