The Study Of Two Kinds Of Nonautonomous Lotka-Volterra Competing Systems

In this paper, three nonautonomous competitive Lotka-Volterra systems are studied,Sufficient conditions for its extinction and permanence are established by comparison theorem and Lyapunov functions of ordinary differential equations.it consists of four chapters.The first chapter focuses on the development of Lotka-Volterra systems and our main work in this thesis.We also give some main lemmas and theorems which will be used in the following.A nonautonomous competitive Lotka-Volterra subsystem without delay is considered in chapter two. Sufficient conditions on the coefficients are given by certain condition to guarantee that all but one of the species are driven to extinction.The corresponding conclusion is proved by constructing proper Lyapunov function.It is shown that some results of the related literatures have been extended.In chapter three,the two species nonautonomous competitive Lotka-Volterra system with impulsive effects is considered. Sufficient conditions for its permanence are established by comparison theorem and Lyapunov functions.In the last chapter,the results of stability and extinction or permanence of the competitive Lotka-Volterra system with delays are mainly explained. Sufficient conditions are obtained for the permanence of the Lotka-Volterra system with infinite delays, its results are regarded as the supplement of the literature [39].