功能反应函数为x^(1/2)的食饵-捕食系统的定性分析

On Qualitative Analysis of Functional Reaction Function X^(1/2) Prey-Predacious System

本文运用Liapunov第二方法，论证了功能反应函数为x～(1/x)的食饵-捕食系统x=x-ax-2~3-x^(1/x)y,βy=-sy+βx^(1/x)y-εy^2唯一正平衡点的稳定性．其次将该系统化为二次微分系统Ⅲ类方程的标准形式，进而研究了极限环的存在唯一性问题．

In this paper,the authors use second liapunov method to prove the stabitity of uniquepositive balance drop which functional reaction function is,x^(1/2) Prey-Predacious system x=x-ax_2~3-x^(1/x)y,y=-sy+βx^(1/x)y-εy^2,and converted this system into the standard form of differential system Ⅲclass, equation of second order thus the authors studies existence and uniquenes question of limit circle.