Colloquium March 28
Date: Friday March 28
Time: 14:30 to 15:30
Place: 216 McBryde
Speaker: Karin Gatermann of Konrad-Zuse-Zentrum für Informationstechnik Berlin
Title: Differential equations with mass action kinetics
Abstract
We investigate differential equations modelling the behavior
of chemical reactions. They are polynomial ordinary differential equations
for the concentrations depending on time.
The structure of the equations is given by two graphs, a directed graph
and a bipartite graph. The reactions form the directed graph.
The goal of stoichiometric network analysis is to understand how
the discrete structures determine multistationarity, stability and
Hopf bifurcation. In particular the existence of several positive
steady state solutions is necessary for reaction-diffusion waves.
I will explain the approach of intersecting a cone with a
deformed toric variety in order to find positive solutions.
Multistationarity appears in a certain range of parameter which is
determined by Groebner bases of deformed toric ideals.
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