Periodic Solutions Of Leslie-Gower Systems With Impulsive And Diffusion

The predator-prey relationship is an important relationship among species interactions.In this paper,a Leslie-Gower system with impulse effect and spatial diffusion is established on the basis of the existing Leslie-Gower system and its dynamic behavior is studied.This paper is divided into six chapters.The first chapter is the introduction introduces the related research work and the research questions of this article;Chapter 2 is the preliminary knowledge to give the basic hypothesis and two main comparison theorems needed in this article,use the upper and lower solutions to prove the existence of the positive invariant set;Chapter3 applies the method of upper and lower solutions and the principle of comparison,to obtain the final boundedness and persistence conditions of the solution of the system,predator extinction conditions and prey extinction conditions;Chapter 4 obtains the existence conditions of the system with a unique positive global asymptotically stable periodic solution by constructing the V function;Chapter 5 carries out a numerical simulation and graphically verifies the theoretical analysis results;Chapter 6summarizes and further researchable issues.