Global convergence in systems of differential equations arising from chemical reaction networks

TL;DR

This paper demonstrates that specific differential equations from chemical reaction networks have invariant subspaces each with a unique attracting equilibrium, ensuring global convergence within those subspaces.

Contribution

It establishes a novel global convergence property for classes of differential equations modeling chemical reaction networks.

Findings

State space is foliated by invariant subspaces.

Each subspace contains a unique equilibrium.

Equilibria attract all initial conditions in their subspace.

Abstract

It is shown that certain classes of differential equations arising from the modelling of chemical reaction networks have the following property: the state space is foliated by invariant subspaces each of which contains a unique equilibrium which, in turn, attracts all initial conditions on the associated subspace.