Chalmers Conferences, 9th European Conference on Mathematical and Theoretical Biology

Generalized mass action systems and positive solutions of polynomial systems with parameters
Georg Regensburger

Last modified: 2014-06-09


Chemical reaction network theory provides statements about uniqueness, existence, and stability of positive steady states of the related dynamical systems for all rate constants. The relevant conditions depend only on the network structure and the stoichiometric subspace. In terms of polynomial equations, they guarantee existence and uniqueness of positive solutions for all parameters.

We discuss an extension of several statements to generalized mass action systems where reaction rates are allowed to be power-laws in the concentrations. In this setting, uniqueness and existence additionally depend on sign vectors of the stoichiometric and kinetic-order subspaces. This is joint work with Stefan Müller.