Dynamical Analysis Of Predator-prey Models With Prey Dispersal In Two-patch Environments

In this paper, we consider the prey dispersal under predator pressure and the prey dispersal caused by intra-specific competition, establish two predator-prey models, then analyze the dynamic behavior of these models. The paper is divided into four chapters.The first chapter is the introduction. We introduce the predator-prey system, the related research progress and the main work of this paper as well as some definitions and lemmas used in model analysis. In the second chapter, we study a predator-prey model with free dispersal and the prey dispersal under predator pressure between two patches. We analyze the sufficient condition for boundary equilibria and the positive equilibrium to be exist and stable, the sufficient condition for the predator population to be persistent and extinct, then investigate the effects of the two types of prey dispersal. In the third chapter, we study a predator-prey model with Holling Type II functional response and nonlinear prey dispersal. We analyze the strong continuity of positive solutions as well as the local stability of the equilibria. In the last chapter, we review and summarize the main contents of this paper, then put forward some idea for further research and expansion.