干扰、恐惧效应和Holling II型的捕食模型的稳定性

Disturbance, Fear Effect and Stability of Predator Model of Holling II

摘要: 本文研究一类具有相互干扰、恐惧效应和Holling II型的Lotka-Volterra捕食模型，分析了解非负性、有界性和系统平衡点的存在性以及平衡点的稳定性，并给出系统持续性的充分条件。还得出恐惧水平的改变对边界平衡点的稳定性没有影响，但对正平衡点有影响的结论；当恐惧因子满足定理时，系统在正平衡点处出现Hopf分支。

Abstract: In this paper, a class of Lotka-Volterra predation models with mutual interference, fear effect and Holling II type are studied, and the existence of non-negativity, boundedness, and system equilibrium points and the stability of equilibrium points are analyzed, and sufficient conditions for system persistence are given. It is also concluded that the change of fear level has no effect on the stability of the boundary equilibrium point, but has an effect on the positive equilibrium point. When the fear factor satisfies the theorem, the system appears a Hopf branch at the positive equilibrium point.