Consider Nonautomous Lotka-Volterra System And Web Sites Competion

In this dissertation, we analyse the stability of the competition model of e-comerce sites, give the numerical simulation of the web sites competition, establish a series of new strategies of the web sites competition. Consider a class of the average growth conditions of three dimensional nonautonomous competitive Lotka-Volterra system. Analyse the enterprise competition based on nonautonomous competitive Lotka-Volterra system, give the numerical simulation of the enterprise competition, and establish a series of new strategies for enterprises.This dissertation have five chapters.In the first chapter, we expound the main work background of Lotka-Volterra system, Lotka-Volterra system which applied in competitive web sites and enterprise competition background, and expound the main results of this thesis.In the second chapter, we study the stability of the equilibrium for the competitive model of e-commerce sites by using the qualititive analysis of the differential equations, and obtain some conditions of stability of the equilibrium. We give the numerical simulation of the system, and discuss the influence of the system parameter. Combining with the analysis and the numerical simulation of the system, we establish a series of new strategies for sites to win.In the third chapter, a three-dimensional nonautonomous competitive Lotka-Volterra system is considered. It is shown that if the growth rates are positive, bounded and continuous functions on, and the averages of the growth rates satisfy certain inequalities, then any positive solution has the property that one of its components vanishes. If one of the above inequalities is changed, then all components of any positive solution has positive infimum.In the fourth chapter, we analyse the enterprise competition based on nonautonomous Lotka-Volterra system, and give the numerical simulation of the system, and discuss the influence of initial value of system. Combining with the analysis and the numerical simulation of the system, we establish a series of new strategies for enterprise to win.Chapter fifth we make a summary and outlook to the contents of this dissertation.