具有Holling II功能反应扩散捕食系统的定性分析

Qualitative Analysis of a Diffusive Predator-Prey System with Holling Type II Functional Response

首先引入一类具有Holling II功能反应和Neumann边界条件的扩散捕食系统,通过本征值研究正平衡点的一致渐近稳定性,并构造V函数给出全局渐近稳定性定理。其次,对于相应的稳定态系统,利用极值原理、Harnack不等式和能量积分推导了先验估计和非常数正解不存在性定理,最后利用单重本征值分支理论讨论了正常数稳态解的局部分支。

The author firstly introduced a diffusive predator-prey system with Holling type II functional re-sponse subject to homogeneous Neumann boundary conditions, presented uniform asymptotic stability via eigenvalues, and also gave global asymptotic stability by constructing a V function. Then, for the corresponding steady state system, prior estimates and theorems about non-existence of non-constant positive solutions were deduced with the help of the maximum principle, the Harnack inequality and energy integration. Finally, local bifurcation from positive constant steady state solution was discussed by using the simple eigenvalue bifurcation theory.