Existence Of Positive Periodic Solutions Of Neutral Impulsive Predator-prey Systems

Population dynamical system is an important research direction of ecological mathematics.Generally,in the study of population dynamical system,many authors studied inherent characteristics of complex biological system by establishing proper mathematical model and combining with the corresponding mathematical theory.It is a kind of very efficacious method in the study of the existence of positive periodic solutions on prey-predator system by using Mawhin coincidence degree theory.In this paper,by using Mawhin coincidence degree theory and some analytical skills,we study the existence of positive periodic solutions for prey-predator competi-tion system with different functional responses.This paper includes three chapters as follows:Chapter 1 introduces the backgrounds and significance of our studies briefly.Fur-thermore,some basic models of population dynamic system are briefly introduced.Chapter 2 discusses a neutral impulsive predator-prey model with Holling-type IV functional response,we get sufficient conditions for the existence of positive periodic solutions to the system.Chapter 3 investigates a neutral impulsive multispecies predator-prey competition dynamic system with Beddington-DeAngelis functional response.By using Mawhin coincidence degree theory and some analytical skills,the existence of positive periodic solutions for the system are obtained.