两种群都有收获率的微分生态系统的定性分析

A qualitative analysis of differential ecosystem with harvesting rates for preys and predators

在食饵种群具有常数收获率的生态系统的基础上,研究了一类捕食种群、食饵种群(有非线性密度制约)同时具有收获率的HollingⅢ类功能反应的生态系统.应用微分方程定性理论,讨论了系统的平衡点,对中心焦点的阶数、稳定性作出了分析,得出了该系统不存在极限环及存在唯一的极限环的条件.仿真结果说明了理论的正确性.

Based on ecosystem with constant harvesting rate for preys,a HollingⅢ functional response system with harvesting rates for preys and predators is studied.The system＇s equilibrium point is discussed with the qualitative theory of differential equations.The order and the stability of the center focus are analysed.It is found that there is no system＇s limit cycle when the given parameter satisfies certain conditions.By using Hopf bifurcation theorem and Zhang Zhifen theorem,the uniqueness of the system＇s limit cycle is proved.Simulation results indicate the efficacy of the method theoretically.It is obtained that the densities of preys and predators are stable under some conditions.