两种群都有收获率的HollingIV类模型的定性分析

Qualitative Analysis of a HollingIV Model with Harvesting Rates for Preys and Predators

针对一类捕食种群进行分析:食饵种群同时具有收获率的HollingIV类功能反应生态系统,其中食饵种群具有非线性密度制约,捕食者无密度制约。应用微分方程定性理论,讨论了这种微分生态系统,研究了系统的平衡点,对中心焦点的阶数,稳定性做出了分析,得出结论:当给定参数满足一定条件时系统不存在极限环,并利用Hopf分支理论证明了该系统极限环的存在性。结果表明:两种群的密度可以保持一种稳定状态。

A HollingIV functional response system with harvesting rates for preys and predators is studied.The system＇s equilibrium points are discussed by using differential equations qualities theory.The order and the stability of the center focus are analysed.The nonexistence of the system＇s limit cycle is obtained if the given parameters satisfy certain conditions.By using Hopf bifurcation theorem,the existence of the system＇s limit cycle is proved.It is obtained that the densities of preys and predators are stable under some conditions.