一类被开发的具有Beddington-DeAngelis型功能性反应的捕食系统的全局稳定性

Global Asymptotic Stability of a Class of Exploited Predator-Prey System with Beddington-DeAngelis Functional Response

利用微分方程比较原理、重合度理论中的Mawhin’s延拓定理和Lyapunov泛函以及Barbalat引理,研究了一类被开发的具有时滞和Beddington-DeAngelis型功能性反应的捕食系统,得到了该系统一致持久和其周期系统存在唯一全局渐近稳定的周期解的充分条件.

By applying comparison theorem of differential equation, Mawhin＇ s Continuation Theorem of coincidence degree theory, Barbalat Lemma and Lyapunov Function, a exploited predator-prey system with time delay and Beddington-DeAngelis functional response is studied. It is proved that the exploited system is uniformly persistent under appropriate conditions. Further, if the system is a periodic one, it can have a strictly positive periodic solution which is global asymptotic stable under appropritions.