具无限时滞和非单调功能性反应捕食系统的多周期解

利用重合度理论中的延拓定理,研究一类具有无限时滞和非单调功能性反应的捕食者-食饵系统正周期解的存在性,得到了两个有界开集和至少存在两个周期正解的充分条件.结果表明,当食饵群负载容纳量和捕食者种群增长率均足够大时,系统将产生生物性多周期振荡。

Multiple Periodic Solution of a Predator-Prey System with Infinite Delay and Non-monotonic Functional Response

sing the continuation theorem based on coincidence degree theory, we studied the existence of positive periodic solutions for a predator prey system with infinite delay and non monotonic functional response. Two bounded open sets were obtained by means of analytic technique and a set of sufficient conditions for this system to have at least two positive periodic solutions was also obtained. It was revealed that when the carryingcapacity of prey species and the increasing rate of predator species are all sufficiently large, the system will bring periodic oscillation of biological nature.