Dynamics Analysis For Modified Leslie-gower Predator-prey Model With Holling Functional Response And Diffusion

In this thesis, we consider the forefront of biological mathematics problem that is Leslie-Gower type predator-prey model with Holling functional response and diffusion to homoge-neous Neumann boundary conditions. The thesis is divided into two chapters,in the first chap-ter, we consider modified Leslie-Gower predator-prey model with Holling II functional re-sponse and diffusion; in the second chapter, we study modified Leslie-Gower predator-preyfood chains with Holling I functional response and diffusion.In the first chapter, we consider the local stability of the positive constant equilibrium bythe linearization method; then we study the non-existence of the non-constant positive solu-tions by means of a priori estimate and energy method; furthermore, we certify the existenceof non-constant positive solutions by using the Leray-Schauder degree theory. In the secondchapter, we discuss the dissipation and persistent of system by using comparison theorem andC0analysis semigroup theory,embedding theorem; we analyze the local stability of the positiveconstant equilibrium and non-negative constant equilibrium by the linearization method, at thesame time we get a interesting conclusion in this section—the positive constant equilibriumis locally asymptotically stable if which exist; we drive the non-existence of non-constantpositive solution by a priori estimate and energy method.