具有分布时滞的恒化器模型的动力学分析

Dynamics Analysis of a Chcmostat Model with Distributed Time Delay

本文建立具有一般功能反应函数和分布时滞的恒化器模型。首先证明了模型解得正性和有界性,然后计算得到基本再生数,分析了细菌灭绝平衡点、无感染平衡点和正平衡点的存在的条件。通过构造Lyapunov函数,得到细菌灭绝平衡点、无感染平衡点的全局稳定性。

In this paper, a chemo stat model with general function and distributed time delay is established. Firstly, the paper proves that the solutions of the model is positive and boundary, then it calculates the basic regeneration number, and lastly analyzes the conditions for bacteria extinction equilibrium point, infection-free equilibrium point and positive equilibrium point. By constructing the Lyapunov function, the global stability of extinction equilibrium point and infection-free equilibrium point are obtained.