Local and Global Stability of Equilibria for a Class of Chemical Reaction Networks (2013)

First Author: Donnell P

Attributed to:  Stability and order preservation in chemical reaction networks funded by EPSRC

Abstract

A class of chemical reaction networks is described with the property that each positive equilibrium is
locally asymptotically stable relative to its stoichiometry class, an invariant subspace on which it lies.
The reaction systems treated are characterized primarily by the existence of a certain factorization
of their stoichiometric matrix and strong connectedness of an associated graph. Only very mild
assumptions are made about the rates of reactions, and, in particular, mass action kinetics are not
assumed. In many cases, local asymptotic stability can be extended to global asymptotic stability
of each positive equilibrium relative to its stoichiometry class. The results are proved via the
construction of Lyapunov functions whose existence follows from the fact that the reaction networks
define monotone dynamical systems with increasing integrals.

Bibliographic Information

Digital Object Identifier: http://dx.doi.org/10.1137/120898486

Publication URI: http://dx.doi.org/10.1137/120898486

Type: Journal Article/Review

Volume: 12

Parent Publication: SIAM Journal on Applied Dynamical Systems

Issue: 2