Persistence of Delayed Complex Balanced Chemical Reaction Networks

Abstract

In this article, we mainly focus on the persistence of delayed complex balanced systems. We first give the ω-limit set theorem for this kind of system which says that ω-limit set can be the single constant positive equilibrium or the set of constant equilibria on the boundaries. In addition, we derive several sufficient conditions to diagnose the persistence of delayed complex balanced chemical reaction network systems equipped with mass-action kinetics based on the situation of the boundary of stoichiometric compatibility class. Then, we can directly obtain that delayed complex balanced systems with two-dimensional stoichiometric subspace are persistent. Furthermore, we prove the abovementioned systems are globally asymptotically stable at the corresponding positive equilibrium if the trajectory starts from a positive initial function. We illustrate the analysis by two numerical examples.