Spatial Dynamics Of Some Modified Leslie-Gower Prey-Predator Model With Shifting Habitats

In this thesis,we mainly study the spatial dynamics of a modified LeslieGower prey-predator model in some shifting habitats and the spatial dynamics of a modified Leslie-Gower prey-predator model with nonlocal dispersal or nonlocal effects under shifting habitats,respectively.The first chapter is mainly reviewed the background and research status of the issues,and introduced the main work of this paper and significance of the study.In Chapter 2,we will study the long time spatial dynamics of a modified Leslie-Gower prey-predator model in shifting habitats where di>0(i=1,2)represent the diffusion rate of the prey and predator,respectively,α,β are positive parameters,ri(·)(i=1,2)is the growth rate function of the prey and predator,respectively.By comparing the spreading speed of species with the different change speed of habitats,we obtained the different conditions of species extinction and continuous spread in the habitats,and focused on the coexistence of the two species.At the end of this chapter,we show the mathematical simulation and analyze the conclusions of this chapter.In Chapter 3,we will discuss the spatial dynamics of a modified Leslie-Gower prey-predator model with nonlocal effects under a shifting habitat where(J*v)(x,t)=∫R(y)v(x-y,t)dy.In this chapter,we mainly use the upper and lower solution method,the comparison principle and the monotone iteration method to describe the different situations of species spreading,survive and extinction of the model.Finally,we prove the existence of equilibrium solution for the Cauchy problem.In Chapter 4,we will consider the spatial dynamics of a modified Leslie-Gower prey-predator model with nonlocal dispersal under shifting habitats where(Ji*u)(x,t)=∫R Ji(x-y)u(y,t)dy,(Ji*v)(x,t)=∫R Ji(x-y)v(y,t)dy(i=1,2).Compared with the classical Laplace diffusion,the integral operator reflects the relationship between the position x and all other positions y so it is a nonlocal concept.By comparing the different spreading speed of species with the speed of environmental worsening,we get the different conditions for three situations of extinction of both species,the existence of one species,coexistence of two species.