Stochastic Characteristics And Optimal Control Of Two Classes Stochastic Chemostat Models With Variable Yield

In this paper,we mainly investigate stochastic characteristics and optimal control of two classes stochastic chemostat models with variable yield.The article includes three 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 chemostat model with variable yield and Monod uptake function is investigated.The environment noises are given by independent standard Brownian motions,and the yield coefficient reflecting the conversion of nutrient to microorganism varies depending on the ambient nutrient.First,we give that the stochastic system has a unique global positive solution by using stochastic Lyapunov function,It(?)'s formula and Gronwall inequality.Second,following strong law of large numbers of Brownian motion and other basic theories,the sufficient conditions for the extinction and strong persistence in the mean of the microorganism are established by studying the stochastic system in detail.Third,by the operator L and a method to determine the existence and uniqueness of stationary distribution,the existence of a unique stationary distribution to the stochastic model is further studied.In addition,some numerical simulations are carried out to illustrate the theoretical results and the influence of the variable yield on the microorganism.In Chapter 3,a stochastic chemostat model with variable yield and Contois uptake function is investigated.The yield coefficient depends on the limiting nutrient,and the environmental noises are given by independent standard Brownian motions.First,by using stochastic Lyapunov function,It(?)'s formula and some important inequalities,the existence and uniqueness of the global positive solution are proved.Second,the stochastic characteristics for the stochastic model are studied,including the extinction of the microorganism,the strong persistence in the mean of the microorganism and the existence of a unique stationary distribution of the stochastic model.Third,the necessary condition of an optimal stochastic control for the stochastic model is established by Hamiltonian function.In addition,some numerical simulations are carried out to illustrate the theoretical results and the influence of the variable yield on the microorganism.In Chapter 4,this paper is summarized and the research work is prospected.