Campuses:

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.