捕食者具有Allee效应和其他食物来源的Leslie-Gower模型的稳定性分析

Stability Analysis of the Leslie-Gower Model for Predator with Allee Effect and Other Food Resource

摘要: 本文研究捕食者具有Allee效应和其他食物来源的Leslie-Gower模型的动力学性质。我们讨论了边界平衡点和正平衡点存在的条件和稳定性。说明了较大的Allee效应会破坏系统的稳定性。当捕食者具有其他食物来源时，系统的动力学性质会变得更加复杂，也就是捕食者具有其他食物来源可能会破坏系统的稳定性。最后通过数值模拟，发现系统会经历Hopf分支并产生极限环。

Abstract: This paper studies the dynamics of the Leslie-Gower model for predator with Allee effect and other food source. We discuss the existence conditions and stability of boundary equilibrium points and positive equilibria. It is shown that the larger Allee effect will destroy the stability of the system. When predators have other food sources, the dynamics of the system becomes more complex, that is, the presence of predators with other food sources may destabilize the system. Finally, through numerical simulation we find that the system experiences Hopf bifurcation and limit cycle exists.