Stability Analysis And Bifurcations Of Tow Kinds Of Discrete Predator-Prey Models

In this thesis,the stability and bifurcation problems of two kinds of discrete predatorprey models are studied.The full text is divided into four chapters.In the first chapter,introduce the research background and significance of the topic,establishe two kinds of discrete predator-prey models and summarize the main work.In chapter 2,we consider a kind of Leslie-Gower discrete predator-prey models with refuge and fear.Judged the stability of equilibrium points by means of the eigenvalue theory and analyzed the bifurcations by means of the central manifold theorem and the bifurcation theory.The sufficient conditions are given to ensure that the predator-prey model produces a Flip bifurcation at the equilibrium point where only the predator exists and a NeimarkSacker bifurcation at the equilibrium point where two species coexist.In Chapter 3,we study a kind of discrete predator-prey models with refuge,fear,and extra food,and analyze the effects of refuge,fear,and extra food on the discrete predator-prey models with Crowley-Martin type functional response.We give the stability of equilibrium points by means of the eigenvalue theory and study the bifurcations by means of the central manifold theorem and bifurcation theory.It was obtained Flip bifurcation occurs at equilibrium point where only the predator exists and equilibrium point where only the prey exists,and Neimark-Sacker bifurcation occurs at equilibrium point where two species coexist.The conclusion and discussion for the work of this thesis are presented in the fourth chapter.