具HollingⅡ型响应函数捕食模型的稳态解

Stable Solution of a Predator-Prey Model with Holling Ⅱ Functional Response

研究了一类非线性反应扩散系统 ,该系统描述了具HollingⅡ型响应函数的捕食模型 ,首先利用正性引理和上下解方法给出了问题解的全局存在性和唯一性 ,接着给出了常微系统和偏微系统稳定性的结果 ,最后用这些结果给出了所讨论问题的全局稳定性 ,并在生物意义上给出解释。

This paper addresses a nonlinear reaction diffusion system, describing a predator-prey model with Holling Ⅱ type functional response. At first Postivity Lemma is used to prove the global existence and uniquiness of this pnablem. And then of the stabilitybetween ODE system and PDE system is set forth. Finally the reslut is demonstrated in the sense of Ecology.