Modelling with Mass-action Kinetics and Beyond

Thursday, March 8, 2007 - 1:30pm - 2:20pm
EE/CS 3-180
Markus Kirkilionis (University of Warwick)
Mass-action kinetics is a powerful tool to describe events created by collission of molecules or individuals in a well-mixed environment giving them locally the same probability to meet each other. Moreover this probability is only dependent on the concentration of the mutual partners.
Mass action systems can be found in chemistry, cell biology, but also game theory and economics. Mathematically this gives rise to dynamical systems of a special type, more specific of polynomial type. I will give an overview how this property can be used to determine different types of bifurcations, for example the ocurrence of bistability, or oscillations via a Hopf bifurcation. All tools will be borrowing methods from algebraic geometry. Finally I will give an outlook what usually goes wrong in the modelling part while using mass-action kinetics if biochemical or cellular molecular events are considered. Finally the talk ends with a fresh look on mass-action kinetics applied to a spatial setting.
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