Existence of Positive Periodic Solutions of a Predator-Prey Diffusive System with Density Restricts and Stage-Structure

In this paper, we study the existence of positive periodic solutions for a predator-prey diffusive system with delayed density restricts and stage structure. 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.