一类恒化器时滞模型的性态分析
Performance Analysis of a Delayed Chemostat Model
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摘要: 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 .Abstract: 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 .
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Key words:
- chemostat model，delay，stability，bifurcation /
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