一类具有时滞的植被–沙模型的Hopf分支

Hopf Bifurcation for a Vegetation-Sand Mod-el with Time Delay

利用Hopf分支理论研究一类具有时滞效应的植被–沙模型。首先分析特征值问题,给出时滞 对正平衡点稳定性的影响及Hopf分支的存在性。其次利用中心流形定理和规范型理论,给出Hopf分支方向和分支周期解稳定性的判定条件。最后借助数值模拟,验证理论分析结果。

A vegetation-sand model with time delay is studied by Hopf bifurcation theory. Firstly, the eigen-valuesare analyzed to obtain the effect of time delay on the stability of positive equilibrium points, and at the same time, the existence of Hopf bifurcation is given. Secondly, by the center manifold theorem and normal form theory, the determination conditions of Hopf bifurcation direction and the stability of periodic solutions are established. Finally, numerical simulations are supplied to verify the theoretical analysis results.