Symbolic Computation Group

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.