一类恒化器时滞模型的性态分析

Performance Analysis of a Delayed Chemostat Model

研究了一类带时滞的恒化器模型,将经典恒化器模型中的微生物营养吸收的功能反应函数一般化.首先利用微分方程的基本理论证明了模型的解的正性和有界性,其次给出了系统的基本再生数以及平衡点存在的条件,再利用特征根方法确定了平衡点的局部渐近稳定性的条件,最后通过构造Lyapunov函数得出了细菌灭绝平衡点和无感染平衡点处的全局渐近稳定性.

In this paper ,we study a delayed chemostat model in which the functional response function of microbial nutrient uptake in the classical chemostat model is generalized .Firstly ,we prove that the solu-tions of the model are positive and bounded by using the basic theories of differential equations .Secondly , we calculate the basic reproduction number of the system and analyze the existence conditions of equilibri-um points .Moreover ,we use the theory of characteristic roots to study the conditions for the local asymp-totic stability of equilibrium points .Finally ,we study the global asymptotic stability of bacterial extinction equilibrium and infection-free equilibrium by constructing Lyapunov functions .