Traveling Wave Solutions And Stability For Predator-Prey Models With Nonlocal Diffusion

With nonlocal diffusion phenomena of the predator-prey is a very important and widespread phenomenon in population ecology,can be described with nonlocal diffusion predator-prey model.The traveling wave solutions can describe the process of species development,mi-gration and invasion,and reveal the changing rule of the species.Therefore,it is of great theoretical and practical significance to study the existence and stability of the traveling wave solution of the predation model with nonlocal diffusion.This thesis is divided into four parts.Chapter 1,we introduce the development of the traveling wave solutions and the main work of this thesis.Chapter 2,we study the existence and stability of traveling wave fronts for a three species cooperation predator-prey model with nonlocal diffusion.where u(x,t)and v(x,t)denote the densities of two cooperative preys at time t and location x,respectively,and z(x,t)denotes the density of the predator at time t and location x.We prove that the traveling wave fronts with the relatively large wave speed are exponentially stable as perturbation in some exponentially weighted spaces,when the difference between initial data and traveling wave fronts decays exponential at negative infinity,but in other locations,the initial data can be very large.The adopted method is to use the weighted energy method and the squeezing technique with some new flavors to handle the nonlocal dispersals.These results have been published in SCI journal Complexity.Chapter 3,we study the existence and stability of traveling wave fronts for a three species competition predator-prey model with nonlocal diffusion.where u(x,t)and v(x,t)stand for population densities of two competitive species at time t and location x,respectively,and z(x,t)denotes the density of the predator at time t and location x.This chapter firstly establishes the existence of traveling wave solutions by means of monotone half-flow theory and upper and lower solutions,explains the suitability of solutions in different solution spaces,then presents the existence and stability theorems of traveling wave solutions,and finally proves that the traveling wave solution of the connection-equilibrium point is globally stable by means of dynamic system method.Chapter 4,we give the conclusions and discussion of this thesis.