Stability Analysis And Periodic Solutions Of Ecological Mathematical Models

The thesis is concerned with periodic solutions of ecology mathematic models and stability.The whole thesis contains four chapters. The first chapter introduces the research background of the thesis,preliminaries and notion,and the main results.Chapter 2 deals with the behavior of solutions of periodic Lotka-Volterra system.The Perisistence and Periodic Solutions obtained by using comparison principles and Brouwer fixed-point theorem.Also,the global asymptotic stability is given by resorting to Liapunov functions.Chapter 3 is to study the existence of positive periodic solutions for a class of Predator-Prey models with multi-delays. Under the suitable conditions,the existence of positive periodic solutions is contained by using Continuation theorem of Concidence degree theory,which generalizes some known results.The final chapter considers a new method to solve Volterra Predator-Prey Models.The iteration algorithm of analytic solutions is constructed by using Adomian's decomposition.