捕食者具有自适应调节的捕食模型的稳定性

摘要

The stability behavior of a predator-prey model with adaptive choice by the predator was studied.The existence of possible equilibriums was discussed;then sufficient conditions for the existence of equilibriums were achieved.A qualitative analysis was carried out to research into the local stability of the equilibriums,and the sufficient conditions were achieved through the linearized stability theorem and Routh-Hurwitz criterion.The persistence of the system was investigated via constructing the Lyapunov function.%研究了捕食者具有自适应调节的捕食模型的稳定性和持久性.讨论了边界平衡态和正平衡态的存在性,得到了各类平衡态存在的充分条件.使用线性稳定性理论和Routh-Hurwitz判定准则研究了各类平衡态的稳定性,获得了各类平衡态稳定的充分条件.通过构造持久Lyapunov函数证明了系统的持久性.