Stefan Müller: Positive equilibria of (generalized) mass-action systems

Essentially every nonnegative ODE model used in chemistry and biology (for example, in ecology and epidemiology) and even in economics and engineering can be written as a reaction network with (generalized) mass-action kinetics. In previous work, we have focused on positive equilibria that are determined by the underlying graph (complex-balanced equilibria).

Here, we consider general equilibria. That is, we study positive solutions to parametrized systems of generalized polynomial equations (with real exponents). We identify the relevant geometric objects of the problem, namely the coefficient polytope and the monomial difference and monomial dependency subspaces. As our main result, we rewrite the polynomial equations in terms of binomial equations on the coefficient polytope. Notably, polynomial inequalities (arising from stability or multistationarity considerations) are also covered by our result.

Joint work with Georg Regensburger.