具有HollingⅡ功能反应函数捕食系统的Hopf分支

Hopf Bifurcation of The Predator-Prey System with Holling's TypeⅡ Functional Response

主要应用微分方程定性理论与分支方法探讨了一类具有HollingⅡ功能函数捕食系统的平衡点与Hopf分支。首先通过相关定性理论对系统奇点性态进行了分析讨论,然后利用Hopf分支理论给出了系统极限环的存在性、唯一性及稳定性的条件。

In this paper, the Hopf Ⅱ bifurcations of the predator-prey system with Holling＇ s Type 11 functional response are investigated by using the qualitative theory of ordinary differential equations （ODEs） and the method of bifurcations. First, the behavior of equilibrium points is discussed by means of the qualitative theory. And then the existence, the uniqueness and the stability of the limit cycles are presented by Hopf bifurcation theory.