具有Beddington-DeAngelis型功能反应函数和线性消耗率的恒化器模型的定性分析

本文研究了一类具有线性消耗率和Beddington-DeAngelis型功能反应函数的恒化器模型。分析了系统平衡点的存在性及局部渐近稳定性, 利用Liapunov-LaSalle不变性原理证明了边界平衡点E₀是全局渐近稳定的。给出了平衡点E₁₀和E₂₀的全局渐近稳定的结论。最后, 对E₀, E₁₀, E₂₀, E_* 4个平衡点的全局渐近稳定性进行了数值模拟。

Qualitative analysis of a chemostat model with Beddington-DeAngelis functional response and linear consumption rate

This paper addressed a type of chemostat model with linear variable yield and Beddington-DeAngelis type functional response. We deliberately analyze the existence and local asymptotic stability of its equilibrium.We also prove that the washout equilibrium E₀ is globally asymptotically stable using Liapunov-LaSalle invariant principle. E₁₀ and E₂₀ are globally asymptotically stable. Numerical simulations are presented to demonstrate the global asymptotic stability of four equilibrium E₀, E₁₀, E₂₀, E_* .