Dynamics Analysis Of Several Stochastic Population Systems

This paper is divided into five chapters. The first chapter we mainly introduce the research background, some of the basic concepts and some of the main theorem about the stochastic biological mathematics.In chapter two, some asymptotical properties of a stochastic non-autonomous predator-prey system with delay and Beddington-DeAngelis functional response are studied. Firstly, the existence of a global solution and stochastically ultimate boundedness are shown. Secondly, we study the global attractiveness under some conditions. Finally, some numerical simulations are introduced to illustrate the main results.In chapter three, we mainly consider an autonomous Lotka-Volterra competitive system with stochastic perturbation and feedback controls. Firstly we show the existence and the uniqueness of the solution by constructed a Lyapunov function. Secondly, under a simple assumption, almost sufficient and necessary conditions for stability in the mean and extinction of each population are established, we can though feedback controls make these endangered species achieve to stability in the mean when the intensity of white noise is small. Finally, some numerical simulations are introduced to illustrate the main results.In chapter four, we discuss the dynamic of an autonomous Lotka-Volterra stochastic competitive system with feedback controls and infinite delays. In the same way, we firstly construct a Lyapunov function to show existence and uniqueness for the global solution of this system. Sufficient conditions which ensure the global stability of the system are considered. Finally, we cite a few examples to further illustrate and test our resultsIn chapter five, we discuss a N-species stochastic competitive system. a sufficient condition is established for each population extinction and stability in the mean.