Dynamical Properties To Two Classes Of Population Models With Impulses And Delays

In this paper,we mainly consider the infinite and limited delayed population competitive system with impulses.Sufficient conditions are obtained for the permanence,global attractivity of solutions,as well as existence of positive periodic solutions and almost periodic solutions by a systematic qualitative analysis.This paper can be divided into three chapters.In Chapter 1,we introduce historical background and development,current state of the research and the main research work of this paper.In Chapter 2,We mainly discuss the permanence,global attractivity of solutions,positive periodic solutions and almost periodic solutions for model with impulses and infinite delay.We obtained the permanence of the system by using comparison theorem and the skills of magnifying and shrinking.My result extend and improve the related literatures.On the based on the boundness of solutions,constructing suitable Lyapunov functions and some analysis techniques prove its global attractivity,using some analysis techniques to obtain existence of almost periodic solutions of the system,at last,using Gaines and Mawhin's continuation theorem to obtain the existence of positive periodic solutions.In Chapter 3,a limited delayed population system with impulses is investigated.We know population development has the time lag,so on the basis of the original reference model joined the time delays,the main method is using the skills of magnifying and shrinking and comparison theorem to get the permanence of solutions,constructing suitable Lyapunov functions and some analysis techniques to prove its global attractivity and existence of almost periodic solutions.