Dynamic Analysis On Some Population Systems

With the development of science, Lotka-Volterra system and Gilpin-Ayala system, as two basic models in population dynamics, play important roles in physical and social science. This thesis is composed of five chapters to consider the persistence, extinction or global exponential stability of above two systems. The results given in this paper improve and extend the corresponding ones in the literatures.In Chapter 1, we introduce the historical background of problems which will be investigated and the main works of this thesis.In Chapter 2, firstly the strong persistence of the following general nonautonomous Lotka-Volterra system is considered,By the above analysis, we consider the following Lotka-Volterra systemThe suficient conditions for the partial permanence and extinction of above system are obtained, which include the corresponding ones in the literatures.In Chapter 3, we mainly investicate in uniform persistence for a diffusive LotkaVolterrasystem with time delay,In Chapter 4, firstly we consider the following single species diffusive systemThe sufficient conditions for the uniform persistence of above system are obtained. Secondly, we propose the following nonlinear diffusive predator-prey systemsome sufficient conditions for the persistence of above system are obtained. Our results improve and extend the corresponding ones in the literatures.Chapter 5 is considered with a Lotka-Volterra system with time delaysome new sufficient conditions for permanence and exponential stability of above systemare obtained.