带有扩散和Holling Ⅱ功能反应的n个斑块捕食食饵系统的一致持久生存和灭绝分析

Permanence and Extinction for One Class of Holling type ⅡPredator-Prey Model with Dispersal among Patches

本文研究了n个斑块带有扩散的捕食食饵系统.通过采用把子系统看成是一个耦合网络的方式,基于图论和Lyapunov函数构造方法给出了捕食食饵系统的正平衡点全局渐近稳定的条件.本文基于该模型,引入HollingⅡ型功能反应于模型中,得到了带有扩散和HollingⅡ功能反应的n个斑块捕食食饵系统的一致持久生存定理和边界平衡点的稳定定理.

In this paper, we investigate a Holling type II predator-prey model with n-patch and dispersal, our main purpose to extend the model by [3] on a predator-prey model with dispersal for prey among n patches to the case of Holling type II functional response. By using the method of permanence and extinction theories, we derive sufficient conditions under which that the system is permanent and the boundary equilibrium of the Holling type II predator-prey model is global asymptotically stable.