Dynamical Behaviors Of Pulse Diffusion Systems And Stochastic Ecosystem

In this paper the population dynamics models have been discussed, based on the traditional ecological differential model, we add in pulse diffusion and stochastic perturbation respectively, then derived impulsive differential equation and the stochastic differential equations. This paper arranged as the following chapters:In chapter1, introduces the research back ground and the main work.In chapter2, a delayed stage-structured predator-prey system with Hassell-Varley type functional response and prey refuge and impulsive diffusion is reseached. Sufficient conditions for the globally attractive of predator-extinction periodic solution are obtained. We also prove that the system is permanent. Furthermore, numerical simulations are presented for the support of our analytical findings.In chapter3, we investigate a stochastic predator-prey model with Beddington-DeAngelis type functional response and ratio-dependent for predator. By ho formula and stochastic comparison theory, we show that there is a unique positive global solution to the model, and we conclude the stochastic model is stochastically permanent and the conditions for species to be extinct are established. Moreover, some properties of the stochastic model with delay are obtained. We also make some numerical simulations to confirm the above theoretical analysis and the rich dynamics phenomenon, which are caused by stochastic perturbation.In chapter4, we summarize the work of this paper and the future research work is prospected.