Global asymptotic stability for a class of nonlinear chemical equations

2007/08/02 by David F. Anderson, Anderson, David F.
Biochemistry, Genetics and Molecular Biology · Engineering · Mathematics · #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #Gene Regulatory Network Analysis #Mathematical Biology Tumor Growth #Stability and Controllability of Differential Equations #math.CA #math.DS

paper · pdf · doi:10.48550/arxiv.0708.0319

2nd version. Have added a connection with extreme points

openalex publication_date 2007/08/02 · arxiv created 2007/11/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a class of nonlinear differential equations that arises in the study of chemical reaction systems that are known to be locally asymptotically stable and prove that they are in fact globally asymptotically stable. More specifically, we will consider chemical reaction systems that are weakly reversible, have a deficiency of zero, and are equipped with mass action kinetics. We show that if for each c ∈ \R_{> 0}^m the intersection of the stoichiometric compatibility class c + S with the subsets on the boundary that could potentially contain equilibria, L_W, are at most discrete, then global asymptotic stability follows. Previous global stability results for the systems considered in this paper required (c + S) ∩ L_W = ∅ for each c ∈ \R^m_{> 0}, and so this paper can be viewed as an extension of those works.

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