Persistence And Periodic Solutions For Several Kinds Of Lotka-Volterra Systems

This thesis of Master is composed of four chapters, which mainly studies the persistence and periodic solutions for several kinds of Lotka-Volterra systems.Chapter 1 introduces the historical background of the problem-researching, the recent development of the research in this field and the main tasks of this thesis.In chapter 2, we study the persistence of a nonautonomous predator-prey system with diffusion and varying time delay using the theory of analysis, we obtain some sufficient conditions for the uniform persistence of the system, which improve and extend the related results in the literatures.Chapter 3 considers the existence and globally asymptotic stability of the positive periodic solutions to diffusive models with periodic coefficients and varying time delay Firstly, by using Brouwer fixed point theorem, we investigate the existence of the positive periodic solutions. Then by establishing Lyapunov functions, we obtain some sufficient conditions for globally asymptotic stability of the positive periodic solutions, which generalize the relevant results in the literatures.In chapter 4, we concern the existence of a nonautonomous periodic system with impulse and infinite delay By employing coincidence degree theory, some sufficient conditions for the existence of positive periodic solutions to the system are established, which extend some known results.