Qualitative Research Of Neutral Lotka-Volterra Competition Model And Neural Networks

Population dynamical system is the most important branch of ecological mathematics, various predator-prey models have great ecological meanings. Many authors studied intrinsic characteristics of some more complicated biological system, for example, by applying the methods of nonlinear analysis, we can obtain the existence of positive periodic solutions. By using the knowledge of ordinary differential equations,we can obtain the dynamic properties of models.In this paper, by using Mawhin coincidence degree theory, fixed point theorems,Krasnoselskii’s fixed point theorem and the method of Lyapunov functions in stability theory of ordinary differential equation, we study the dynamic behavior of several population dynamical system. This paper includes four chapters as follows:Chapter 1 introduces the backgrounds and significance of our studies, main work of this paper, preparing knowledge.Chapter 2 investigates a neutral delayed Lotka-Volterra competition system with impulsive. By using Comparison theorem of differential equation and Mawhin coincidence degree theory, the extinction of partial species and the existence of positive periodic solutions for system are obtained. We extend some results in references.In Chapter 3 a neural networks with neutral delays is investigated. We obtain sufficient conditions for the existence and uniqueness of almost periodic solutions to system, by using exponential dichotomy and fixed point theorem.Chapter 4 discusses a neural network with neutral delays. By using Comparison theorem of differential equation, Lyapunov function method and Krasnoselskii’s fixed point theorem, sufficient conditions which guarantee the existence and global attractivity of positive periodic solutions of the system are obtained.