Symbolic Computation Group

David R. Cheriton School of Computer Science
University of Waterloo, Waterloo, Ontario, Canada

Symbolic Computations for Chemical Reaction Systems
Karin Gatermann, Konrad Zuse Centrum, Berlin
Friday, November 2, 2001, at U. of Waterloo.

Abstract:

Many chemical reaction systems are described by mass action kinetics which is a system of ordinary differential equations given by polynomials. The structure of these polynomials are given by two graphs, a directed graph and a bipartite graph. Thus the steady states are given as the solutions of a system of sparse polynomials with a lot of structure.

The algebraic techniques of sparse polynomials will be applied. I will show how the Hermite normal form decouples some special sparse polynomial systems into independent systems. That means a nice basis of the lattice is computed. I will show how Groebner bases of special ideals (toric ideals) can be used to solve the system leading to special algorithms. The key idea is the intersection of a toric variety with a convex polyhedral cone in order to find real solutions. Finally, I will mention some dynamical aspects. A criterion to decide stability of all solutions will be presented and Hopf points will be investigated. Again computational algebraic aspects are discussed.

 

Last modified on Sunday, 04 November 2012, at 20:42 hours.