具有非单调功能反应食饵捕食模型的分支分析

Bifurcation Analysis of Predator-prey Model with Non-monotonic Functional Response

考虑具有非单调反应功能函数食饵捕食系统的动力学行为,利用线性化的思想以及Hopf分支定理分析常微分系统以及反应扩散系统在正常数平衡解(u1,v1)处经历的Hopf分支的分支方向与分支周期解的稳定性,通过对比给出空间扩散对系统稳定性的影响.

Considering the dynamic behavior of a prey-predator system with non-monotonic response function,directions of Hopfbifurcations and stabilities of periodic solutions that the ordinary differential system and reaction-diffusion system experience at the positive constant steady state（u1,v1）,are analyzed mainly by the idea of linearization and Hopf bifurcation theorem.The effect of spatial diffusion on the stability of the system is given by contrast.