一类比率型捕食系统的定性分析

Qualitative Analysis of a Ratio-Dependent Prey Model

研究一类比率型捕食者-食饵模型{dt/dx=x（a-bx）-cx^2y/x^2＋my^2 dy/dt=y（-r＋dx^2/x^2＋my^2）应用微分方程定性理论，得出该系统极限环的存在性与正平衡点的全局渐近稳定性的充分条件。

A ratio-dependent predator-prey model is investigated. By using the qualitative theory of ordinary differential equations, sufficient conditions are obtained for the existence of limit cycles and the global stability of the positive equilibrium to the system.