具有Allee效应和Holling-IV型功能反应的修正Leslie-Gower模型的分支分析

Hopf Bifurcation of a Modified Leslie-Gower Predator-Prey System with StrongAllee Effect and Holling Type-IV Functional Response

本文在带有Allee效应和Holling-IV型功能反应的修正Leslie-Gower 捕食者-食饵模型中, 研究稳 定性与各种分支。 首先讨论平衡点的局部渐近稳定性,然后分析跨临界分支,以及以Allee效应参 数m为分支参数的Hopf分支,给出分支存在的条件, 根据定理得出分支的方向及分支周期解的稳 定性。 最后,通过数据模拟验证结论的准确性。

In this paper, we investigate the stability and bifurcations of a modified Leslie-Gower predator-prey system with Holling type-IV functional response and strong Allee effect. First, we use the linearization analysis and bifurcation theory, the local asymptotic stability of the equilibrium points are discussed, and then the condition of the existence of bifurcations is given by choosing m as the bifurcation parameter. On addition, using the canonical theory and the central manifold theorem, the direction of Hopf bifurcation and the stability of periodic solution of bifurcation are analyzed. Finally, the accuracy of the conclusion is verified by numerical simulation.