具有恐惧效应及修正的Holling-Ⅱ捕食者-食饵模型动力学分析

Dynamic Analysis of a Predator-Prey Model ofHolling-Ⅱwith Fear Effect and Modification

利用微分方程的特征值理论、 Poincare-Bendixson环域定理和Hopf分支理论分析具有恐惧效应及修正的Holling-Ⅱ捕食者-食饵模型,给出该模型平衡点的稳定性,并证明该模型具有稳定的极限环以及在共存平衡点处会出现Hopf分支.结果表明,恐惧效应和修正的Holling-Ⅱ函数对系统稳定性有显著影响.

By using the eigenvalue theory of differential equations,Poincare-Bendixson ring theorem and Hopf bifurcation theory,we analyzed the predator-prey model of Holling-Ⅱwith fear effect and modification,gave the stability of the equilibrium point of the model,and proved that the model had stable limit cycles and Hopf bifurcations appeared at coexistence equilibrium points.The results show that the fear effect and the modified Holling-Ⅱfunction have significant effects on the stability of the system.