具有群体效应和时滞的扩散捕食-食饵系统的Hopf分支

HOPF BIFURCATION OF A DIFFUSIVE PREDATOR-PREY MODEL WITH HERD BEHAVIOR AND DELAY

研究了一类具有群体效应和时滞的扩散捕食-食饵系统的Hopf问题。首先,通过分析特征方程,讨论了该系统正平衡点的稳定性和Hopf分支的存在性。然后,利用Faria规范型和偏泛函微分方程中心流形定理,获得了决定Hopf分支性质的计算公式。最后,通过数值模拟,得到了该系统的稳定空间周期解。

We investigate spatiotemporal dynamics problem of a diffusive predator-prey model with herd behavior and delay.Firstly,the stability of the positive equilibrium is discussed by analyzing the corresponding characteristic equation.Furthermore,the formula determining the properties of the Hopf bifurcation are obtained by applying the Faria normal form and the center manifold argument for partial functional differential equations.Finally,some numerical simulations are carried out and we obtain the stable spatial periodic solutions.