一类具扩散和时滞的捕食食饵模型稳定性及分支分析

Stability and Bifurcation of A Diffusive Predator-prey System with Delay Effect

研究了一类具Beddington-DeAngelis功能项的捕食食饵系统受扩散和时滞影响的动力学行为.首先由抛物方程比较原理得到边界平衡点的全局稳定性和不稳定性;然后以时滞为参数,研究唯一正常值平衡点的稳定性及Hopf分支的存在性;最后数值模拟验证了理论结果.

A diffusive predator-prey system with Beddington-DeAngelis type and delay is considered. Global stability or instability of the boundary equilibria is investigated by the comparison principle of the parabolic equations. The stability of the unique positive steady state and the existence of Hopf bifurcation are studied in detail, with the delay as a parameter. Finally, some numerical simulations are given to illustrate the theoretical results.