具有任意时滞的复杂平衡动力系统的半稳定性
Semistability of complex balanced kinetic systems with arbitrary time delays
摘要：
本文介绍了一类由质量作用型反应网络模型导出的时滞动力学系统。我们定义了时滞正化学计量相容性类和复杂平衡时滞动力学系统的概念。我们证明了这类模型在时滞正化学计量相容类内平衡解的唯一性。在我们的主要结果中，我们利用适当的Lyapunov-Krasovskii泛函和LaSalle的不变原理证明了具有任意时滞的复杂平衡系统平衡解的半稳定性.由此，我们得到了每一个正的复平衡解相对于其正的化学计量相容类是局部渐近稳定的。
英文摘要：
In this letter we introduce a class of delayed kinetic systems derived from mass action type reaction network models. We define the time delayed positive stoichiometric compatibility classes and the notion of complex balanced time delayed kinetic systems. We prove the uniqueness of equilibrium solutions within the time delayed positive stoichiometric compatibility classes for such models. In our main result we prove the semistability of the equilibrium solutions for complex balanced systems with arbitrary time delays using an appropriate Lyapunov-Krasovskii functional and LaSalle's invariance principle. As a consequence, we obtain that every positive complex balanced equilibrium solution is locally asymptotically stable relative to its positive stoichiometric compatibility class.
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