The Study Of Some Classes Of Predator-prey System With Diffusion And Impulsion

In this paper, we mainly study the dynamics of some classes of predator-prey system with diffusion and impulsion. The article includes four chapters.The preface is in chapter1, we introduce the research background of this article, the main task and some important preliminaries.In Chapter2, a class of predator-prey system with impulsively diffusive prey between two patches is proposed, predator-prey relationship conform to the Holling II functional response and the predator species with stage-structured. Using comparison theorem of impulsive equation, we obtain the globally attractive condition of predator-extinction periodic solution of the system. We also show the system is permanent by the theory of impulsive delay differential equation.In Chapter3, an impulsive two species periodic Lotka-Volterra predator-prey system with Leslie functional response in a patchy environment is studied, in which the prey species can disperse among two different patches and predator species is confined to one patch. Using comparison theorem of impulsive equation, we obtain the conditions for the permance and extinction of the predator-prey system. We also obtain the existence, uniqueness and the global stability of the positive periodic of the system by constructing suitable Lyapunov functionals.In Chapter4, a class of predator-prey system with impulsively diffusive and Gompertz model prey between two patches is studied,in which the predator species with two time delays is involved. Using the discrete dynamical system determined by the stroboscopic map and some theories of function, we obtain the exact predator-extinction periodic solution. We also show the globally attractive condition of predator-extinction periodic solution and permance of the system.