具有避难所的Holling-Tanner捕食者-食饵扩散模型的稳定性与Hopf分支分析

Stability and Hopf Bifurcation Analysis ona Diffusion Holling-Tanner Predator-PreyModel with Prey Refuge

摘要: 本文研究一类具有避难所的 Holling-Tanner型捕食者-食饵模型。 首先分析了常微分系统下平衡 点的稳定性，然后通过分析扩散模型平衡点的特征方程，讨论正平衡点的局部稳定性以及Hopf分 支存在的条件。 结果表明：避难所会导致Hopf分支产生，产生空间齐次周期解，扩散的加入会创 造新的Hopf分支点，产生空间非齐次周期解。这说明设立适当的食饵避难所有助于物种共存。

Abstract: In this paper, a Holling-Tanner predator-prey model with diffusion and prey refuge is considered. Firstly, the stability of the equilibrium points under the ordinary differential system is analyzed. Secondly, the local stability of the positive equilibrium point and the conditions for the existence of the Hopf branch are discussed by analyzing the characteristic equations of the equilibrium point of the diffusion model. The results show that the refuge will lead to the Hopf bifurcation and produce the spatial homogeneous periodic solution, and the addition of diffusion will create new Hopf bifurcation points and produce the spatial non-homogeneous periodic solution. This indicates that the establishment of appropriate prey refuge will be conducive to the coexistence of species.