一类改进的Leslie-Gower模型平衡态解的稳定性分析

The analysis of equilibrium state solutions about a modified Leslie-Gower model

研究食饵种群具有Crowley-Martin功能反应项和捕食者种群带有经典的Leslie反应项的一类改进的Leslie-Gower模型.首先给出模型平衡解的先验估计,其次研究模型常数正解的存在与唯一性条件,再利用卡尔丹公式解出常数正解值.最后通过构造Lyapunov函数,讨论其常数正解的全局渐近稳定性.

A modified Leslie-Gower model with Crowley-Martin functional response in prey species and classical Leslie dependant functional response in predator species is studied.Firstly,prior estimates of equilibrium state solutions are obtained.Secondly,conditions about the existence and unique of the model′s constant solutions are studied,then the constant solutions are solved by Girolamo Cardano formula.Finally,the global asymptotic stability of the constant solutions is discussed by structuring Lyapunov function.