具有恐惧效应的捕食者-食饵系统的全局动力学

Global Dynamics of a Predator-Prey Model With Fear Effect

为了研究恐惧效应对系统动力学行为的影响,建立了一个具有恐惧效应和HollingⅢ型功能反应的捕食者食饵模型.利用线性化方法和Dulac-Bendixson定理对平衡点的局部及全局稳定性进行了分析;给出了系统发生Hopf分岔的条件,讨论了模型周期解的方向和稳定性;并研究了模型的持久性.利用数值模拟验证了理论分析.结果表明,增强恐惧效应可以排除周期解,有利于系统的稳定.

To study the impact of fear effect on the dynamics of the system,a predator-prey model with fear effect and HollingⅢtype functional response was established.The local and global stability of the equilibria were studied by the linearization and Dulac-Bendixson theorem.The conditions for the Hopf bifurcation were given,the direction and stability of the periodic solutions were discussed.The permanence of the model was also investigated.Numerical simulation was performed to substantiate our analytical findings.It shows that high levels of fear can stabilize the system by excluding the existence of periodic solutions.