The Existence Of Periodic Solutions For Two Population Models

As an important branch in mathematical biology research,the development of population dynamics system has been widely concerned,among which the differential dynamic equation can be used to analyze the objective phenomenon and the rule of biology.By establishing mathematical model,we can find the relationship between various populations and the ecological environment,which can enable us to well un-derstand and explain the complex biological problems and physical phenomena.The coincidence degree theory is a significant method to study many biological mathemat-ics problems.It has become a very important research direction that through applying coincidence degree theory,we can establish the existence of positive periodic solutions for biological dynamic systems and predator-prey systems with harvesting term.In this paper,by using Mawhin coincidence degree theory and some analytical skills,we study the existence and permanence of periodic solutions of this system.This paper includes three chapters as follows:Chapter 1 discusses the backgrounds and significance of our studies,main work of this paper,preparing knowledge.Chapter 2 investigates a predator-prey model with Leslie-Gower functional re-sponse and harvesting terms.we obtain the existence and permanence of the periodic solutions by using Mawhin coincidence degree theory.Chapter 3 discusses a neural delayed ratio-dependent Lotka-Volterra predator-prey model.By using Mawhin coincidence degree theory,we establish the existence result of the periodic solutions.