Permanence And Global Attractlvity For Nonautonomous N Species LV Competitive System With Delays And Impuls

Lotka-Volterra competitive model is one of the most famous models in the dynamics of biological mathematics,it is an important question and the frontier problem in the research of biological mathematics.In this paper,we mainly study the dynamic behavior of a class of nonautonomous N-species Lotka-Volterra competitive systems with delayed and impulsive effects.By using differential equation with impulsive comparison theorem and Lyapunov function,Schauder fixed point theorem,we obtain the sufficient conditions of the existence of positive solution,permanence,global attractivity of the Lotka-Volterra competitive system.A brief description of the organization of the thesis is as follow.In chapter 1,by using differential equation with impulsive comparison theorem,the Lagrange Mean-Value Theorem and Lyapunov function,firstly,we can obtain the sufficient conditions of the permanence and global attractivity of a species Lotka-Volterra system.In chapter 2,from the conclusion in chapter 1,by using differential equation with impulsive comparison theorem and Lyapunov function,we obtain the permanence and global attractivity of N-species Lotka-Volterra competitive system.At the:same time,by using Schauder fixed point theorem,we give the existence of the positive solutions of N-species Lotka-Volterra competitive system.In chapter 3,we give an example to show the effectiveness and feasibility of our maim result.