Dynamical Behaviors Of Impulsive Differential Systems And Stochastic Ecosystem

In this paper the population dynamics models have been discussed, based on the traditional differential model, we add in impulse and stochastic perturbation respectively, and thus we propose the impulsive differential system and the stochastic differential equations. This paper arranged as the following chapters:In chapter1, the background of the research is given, and the major work of this paper is introduced.In chapter2, a mutual interference age structured predator-prey model with disease in the prey and two impulses for integrated pest management is disused. By using comparison theory and Floquet theorem, the sufficient conditions for the global stability of the susceptible pest-eradication periodic solution and the permanence of the system are obtained, and then rich dynamic phenomena such as bifurcation and chaos and so on were showed by numerical simulation.In chapter3, an impulsive predator-prey system with varying delay is proposed, by using coincidence degree theory, the existence of T-periodic solution is given, and numerical simulation is also used to verify the research.In chapter4, we investigate the stochastic permanence and stationary distribution of a stochastic predator-prey system with Beddington-DeAnglis, by using Ito’formula and stochastic comparison theory, we show that the system admits unique positive global solution, and the stochastic model is stochastically permanent and there is a stationary distribution. Numerical simulation is also used to verify the research.In chapter5, we summarize the work of this paper and envisage the research in the future.