ABSTRACT

In this paper, a diffusive predator–prey model with Holling type II (Michaelis–Menten) functional response and a protection zone for prey is investigated. Dynamics and steady state solutions of the system are analyzed. We give the a priori estimates and obtain the nonexistence of nonconstant positive solution as the diffusion coefficients are large enough. Moreover, we demonstrate the existence and stability of nonconstant steady state solutions branching from constant semi-trivial solution by using bifurcation theory.

中文翻译：

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具有猎物保护区的Holling II型猎物-捕食系统动力学

摘要

在本文中，研究了具有 Holling II 型（Michaelis-Menten）功能响应和猎物保护区的扩散捕食者 - 猎物模型。分析了系统的动力学和稳态解。由于扩散系数足够大，我们给出了先验估计并获得了非常数正解的不存在。此外，我们利用分岔理论证明了从恒定半平凡解分支出来的非恒定稳态解的存在性和稳定性。