Existence Of Periodic Solutions For Delayed Predator-Prey Differential Systems With Impulse

The predator-prey models are of great importance in the population dynamics,which attract considerable attention in ecological and biological fields.Generally,in the study of population dynamical system,many authors studied inherent characteristics of com-plex biological system by establishing proper mathematical model and combining with the corresponding mathematical theory.In this thesis,by the using Mawhin's continuation theorem,some analytical skills and the basic theory of impulsive differential equations,we study the existence of positive pe-riodic solutions for prey-predator competition system with different functional responses.This paper includes four chapters.Chapter 1 introduces the backgrounds and significance of our studies,main work of this paper,and preliminary knowledge.Chapter 2 discusses a neutral impulsive predator-prey model with Holling-type IV functional response and mutual interference.By using the Mawhin's continuation theorem and some analytical skills,we get sufficient conditions for the existence of positive periodic solutions to the system.And we perform numerical simulation to support our main results.In this chapter,We generalize the general model with Holling? to the time delay model on the basis of the known results.Chapter 3 investigates a neutral impulsive predator-prey model with monotone func-tional responses.And we consider the effection of variable delay for the model.By using the Mawhin's continuation theorem and some analytical skills,the existence of positive periodic solutions of the system is obtained.We extend some known results without im-pulse.In chapter 4,we give some conclusions and prospects of this article.