Dynamic Analysis Of A Stage-structured Predator-prey Reaction-diffusion System With Harvesting

In recent years,reaction-diffusion theory has been widely used to study the predator-prey sys-tem.Because of population's distribution in nature,it is important to study the diffusion of space.And in the aspect of social ecology,for human's exploitation on the population in the natural ecosys-tem,population changes have also been affected by human behaviors.Considering that many species have experienced juvenile stage and develop to the adult stage,this paper will study population dy-namics of predator-prey diffusion system with age structure and harvesting.Chapter 1 introduces the international background and academic achievements of the predator-prey system,and briefly summarizes the main contents and methods of this paper.In Chapter 2,we consider the following predator-prey system:(?)where (?)are the dcnsities of prcy population,the immature predator and mature predator population at position x at time l,respectively.First,we analyse the corresponding characteristic equations and obtain the local stability of constant equi-libria.Then we establish the existence of traveling wave solution by the upper-lower solution and Schauder's fixed point theorem,generalizing the results of the existing literatures.Chapter 3 considers the following systems:(?)where (?)represent the densities of prey population,the immature predator and mature predator population at position x at time t,respective-1y.We obtain the stability of the constant equilibria and the existence of traveling wave solution of this system.Finally,we summary the research of this paper and clarify the direction of future research.