Study On Dynamical Behaviors Of Two Stochastic Chemostat Models With Variable Yield

In this paper,we mainly study on asymptotical behavior of a chemostat model with variable yield.The article includes four chapters.The preface is in chapter 1,we introduce the research background of this article,the main task and some important preliminaries.In Chapter 2,a stochastic differential equations chemostat model with variable yield and linear growth function is considered.First,we verify that there is a unique global positive solution of the stochastic system.Second,by the stochastic Lyapunov function and It(?) formula,we find that the sufficient conditions of the extinction and persistence of the microorganism,in addition,the existence on the stationary distribution of the stochastic system is studied.Finally,computer simulations are carried out to illustrate the obtained results and the effect of variable yield on the microorganism.In Chapter 3,another stochastic differential equations chemostat model with variable yield and Monod growth response function is considered.First,we verify that there is a unique global positive solution of the stochastic system.Second,by the stochastic Lyapunov function and It(?) formula,we find that the sufficient conditions of the extinction and persistence of the microorganism,in addition,the existence on the stationary distribution of the stochastic system is studied.Finally,computer simulations are carried out to illustrate the obtained results and the effect of variable yield on the microorganism.In Chapter 4,the main work of this paper is summarized and the future research work is prospected.