一类时间离散捕食者-食饵系统中的分岔研究

Neimark-Sacker Bifurcation and Route to Chaos in a Time-Discrete Predator-Prey System

讨论了具有比率依赖型功能反应函数以及捕食者具有可替换食物源特征的时间离散捕食者-食饵系统的稳定性和Neimark-Sacker分岔.通过Jury判据确定了离散系统不动点的稳定性条件;运用中心流形定理和分岔理论分析了Neimark-Sacker分岔的存在性条件;通过数值模拟揭示了由Neimark-Sacker分岔所引起的通往混沌的路径以及混沌路径上的倍周期过程.

This research investigates the stability and Neimark-Sacker bifurcation of a time-discrete predator-prey system,which is characterized by ratio-dependent functional response and the existence of alternate food resources for the predator.Via the Jury criterion,the stability conditions of fixed points of the discrete system are determined.The existence conditions of the Neimark-Sacker bifurcation are analyzed with the center manifold theorem and the bifurcation theorem.Numerical simulations reveal a route to chaos induced by the Neimark-Sacker bifurcation and a period-doubling process in the route.