利用重合度理论中的延拓定理,研究了一类具有双密度制约和Non-Monotonic型功能反应的捕食者-食饵扩散系统正周期解的存在性问题。运用分析技巧获得了一个有界开集和至少存在一个周期正解的充分条件。揭示了当食饵群负载容纳量和捕食者种群增长率均足够大时,系统将产生生物性周期振荡现象。

In this paper,by means of the continuation theorem based on coincidence degree theory,we study the existence of positive periodic solutions for a predator-prey diffusive system with double density restricts and non-monotonic type functional response.One bounded open sets are obtained by using analytic technique and a set of sufficient conditions for this system to have at least one positive periodic solution is obtained.The phenomenon is revealed that when the carrying capacity of prey species and the increasing rate of predator species are all sufficiently large,the system will bring periodic oscillation of biological nature.