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SIAMAM
2008

Global Asymptotic Stability for a Class of Nonlinear Chemical Equations

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Global Asymptotic Stability for a Class of Nonlinear Chemical Equations
We consider a class of nonlinear differential equations that arises in the study of chemical reaction systems 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 Rm >0 the intersection of the stoichiometric compatibility class c + S with the subsets on the boundary that could potentially contain equilibria, LW , are at most discrete, then global asymptotic stability follows. Previous global stability results for the systems considered in this paper required (c + S) LW = for each c Rm >0. Key words. chemical systems, deficiency, global stability, persistence, Petri nets AMS subject classifications. 37C10, 80A30, 92C40, 92D25, 92E10, 93D20 DOI. 10.1137/070698282
David F. Anderson
Added 14 Dec 2010
Updated 14 Dec 2010
Type Journal
Year 2008
Where SIAMAM
Authors David F. Anderson
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