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SIAM J. APPL. MATH. c 2008 Society for Industrial and Applied Mathematics
Vol. 68, No. 5, pp. 14641476
GLOBAL ASYMPTOTIC STABILITY FOR A CLASS OF
NONLINEAR CHEMICAL EQUATIONS
DAVID F. ANDERSON
Abstract. 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
1. Introduction. This paper is motivated by the consideration of a class of
