一类捕食者-食饵模型的全局拓扑结构分析

Global topological structure analysis of a class of prey-predator models

利用微分方程定性理论,对一类具有密度依赖死亡率和比率依赖功能反应函数的捕食者-食饵模型进行系统轨线的全局结构分析.通过Poincaré变换,确定系统的无穷远奇点个数及其类型,利用全局结构图对模型在第一象限(包含边界)的各类奇点(包括有限和无穷)进行了系统分析.

The global structure of the system trajectory is analyzed for a class of predator-prey models with density-dependent and ratio-dependent functional response by using qualitative theory of differential equations.The number and types of critical point at infinity are determined by Poincaré map,and critical points(including finite and infinite) in the first quadrant(including boundary) of the model are systematically analyzed by using global structure diagram.