Studies On Nonautomous Lotka-Volterra System And Its Applications

In this paper, firstly, the permanence and extinction of nonautonomous two dimensionalcompetitive Lotka-Volterra system are considered, the results of the counterpart periodic systemare extended, and the average conditions for the principle of competitive exclusion on two speciesare given. Then, the cooporative Lotka-Volterra model for two scenic spots is established, thestability of the equilibria of the model are analysed, and the numerical simulations and a seriesof management strategies of scenic spots are given.This paper have four chapters.In the first chapter, the background and the current situation of the development of Lotka-Volterra system is introduced. First, the average conditions for the principle of competitiveexclusion in two dimensional nonautonomous competitive system are discussed, and the compe-tition and cooperation of scenic spots is introduced. Then, the main results of this thesis aregiven.In the second chapter, a nonautonomous two dimensional competitive Lotka-Volterra systemis considered. The permanence and extinction are studied, the results of the counterpart periodicsystem are extended, and average conditions are given to guarantee the principle of competitiveexclusion in the system.In the third chapter, a cooperation mathematical model of scenic spots with the relationof cooperation is presented. First, the stability of the equilibria for the cooperation model areanalysed, the efects of the parameters on the model are discussed and the numerical simulationsof the model are given. Then, by the theoretical results, the main factors are discussed forafecting the development of the scenic spots. Finally, a cooperation model is given for morethan two scenic spots.In the fourth chapter, our main results are summarized, and the studying plans in the futureare discussed.