具有恐惧效应的扩散捕食-食饵系统的动力学行为

The Dynamic Behavior of Predator-Prey Diffusion System with Fear Effects

本文研究具有恐惧效应的扩散捕食-食饵系统的动力学行为.对于局部系统,首先证明对于任意给定的非负初始值,系统的解是非负且有界的,其次讨论系统非负平衡点的存在性和局部稳定性,通过构建Dulac函数得到正平衡点全局渐近稳定的条件;对于反应扩散系统,研究Hopf分支和图灵分支的存在性;在Hopf分支存在的情况下,利用中心流形定理和规范型理论得到Hopf分支的稳定性和方向.最后通过数值模拟验证理论结果的正确性,展示系统具有丰富的动力学行为.

In this paper,we investigate the dynamic behavior of a predator-prey diffusion system with fear effects.For the local model,the existence and stability of the nonnegative equilibria of the system are obtained.For reaction-diffusion system,the existence condition of Hopf bifurcation and Turing bifurcation are studied.In the case of Hopf bifurcation,by using the center manifold theory and normal form method,we establish the bifurcation direction and stability of bifurcating periodic solutions.Finally,the correctness of the theoretical results is verified by numerical simulations,which shows that the system has rich dynamic behavior.