一类两个正平衡点的生态捕食模型的定性分析

Qualitative Analysis of a Volterra Predator Prey System under Two Equilibrium Points

本文对Ｖｏｌｔｅｒｒａ捕食模型ｘ＝ａｘ（ｘ—Ｌ）（ｋ—ｘ）一ｂｘｙ，ｙ＝—ｃｙ＋ｄｘｙ—ａｙ２在具有两个正平衡点的情况下进行定性分析。讨论平衡点的类型，Ｈｏｐｆ分支问题，鞍点分界线的相对位置，极限环的存在性。对于解释一些生态现象，有一定的参考价值。

in this paper,we qualitatively analyse the Volterra Predator-Prey system x=ax(x -L)(k-x)-bxy,y=-cy+dxy - ay￣2 under two equilibrium points.We discuss the types of the equilibrium points,Hopf bifurcation,saddle separate relation place.the existence of limit cycles.Some conclusions of the paper can be used to explain some ecological phenomena.