On the steady states of weakly reversible chemical reaction networks

TL;DR

This paper proves that weak reversibility in chemical reaction networks guarantees the existence of steady states in each positive compatibility class and provides an index formula for these equilibria.

Contribution

It establishes a fundamental link between network structure and the existence of equilibria, introducing an index formula for steady states.

Findings

Weak reversibility ensures equilibrium existence in all positive classes.

An index formula for equilibria is derived.

The results connect network topology with dynamical behavior.

Abstract

A natural condition on the structure of the underlying chemical reaction network, namely weak reversibility, is shown to guarantee the existence of an equilibrium (steady state) in each positive stoichiometric compatibility class for the associated mass-action system. Furthermore, an index formula is given for the set of equilibria in a given stoichiometric compatibility class.