The Existence Of Periodic Solution And Its Related Problems

In this thesis, we study the existence of periodic solution and its related problems of three different ecosystems. Based on Mawhin's coincidence degree, spectral theory and Lyapunov functional. Some new estimation techniques are used, and some new results are obtained. This paper has four chapters.In chapter 1, we briefly introduce the related research background, summarize the research motivation and possible difficulty appears duo to study of the ecological systems, and some definitions and lemmas are introduced in this chapter.In chapter 2, we study the periodic solution of a higher dimensional competition system with feedback controls. By means of matrix spectral theory and Mawhin's coin-cidence degree, the existence of periodic solution of such system are obtained, the results obtained with a certain theoretical and practical significance. By making appropriate transformation, constructing Lyapunov functional, some conditions are examined for the global stability of the periodic solution.In chapter 3, we consider the periodic solutions and stability of a stage-structured plant hare model with toxin-determined functional responses, and we can obtain some sufficient conditions. Our method is based on Mawhin's coincidence degree and novel estimation techniques for the a priori bounds of unknown solutions to Lx = ?Nx.In chapter 4, we apply the periodic solutions of a nonautonomous predator-prey model with incorporating a constant refuge. Our results generalize the results of relevant literatures.