Persistence of Delayed Complex Balanced Chemical Reaction Networks

• 成果类型: Article
• 署名作者: Zhang, Xiaoyu; Gao, Chuanhou
• 署名单位: Zhejiang University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.2999321
• 发表日期: 2021
• 页码: 1658-1669
• 关键词: Chemical reaction network (CRN); complex balanced; mass-action system (MAS); persistence; time delay

摘要

In this article, we mainly focus on the persistence of delayed complex balanced systems. We first give the omega-limit set theorem for this kind of system which says that omega-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.