Weakly reversible mass-action systems with infinitely many positive steady states

TL;DR

This paper demonstrates that weakly reversible mass-action systems can possess infinitely many positive steady states, linking network operations to polynomial zeroes in the system's differential equations.

Contribution

It establishes the existence of infinitely many positive steady states in weakly reversible systems and connects network operations to polynomial factors in the differential equations.

Findings

Weakly reversible systems can have a continuum of steady states.

Reversible systems with a single connected component also exhibit this property.

The polynomial zeroes determine the steady states.

Abstract

We show that weakly reversible mass-action systems can have a continuum of positive steady states, coming from the zeroes of a multivariate polynomial. Moreover, the same is true of systems whose underlying reaction network is reversible and has a single connected component. In our construction, we relate operations on the reaction network to the multivariate polynomial occurring as a common factor in the system of differential equations.