The Study Of Some Classes Of Stochastic Chemostat Models With Parameter Interferences

In this paper, we mainly study the dynamics of some classes of chemostat models with white noises in parameters. 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, This section deals with the problem of the single-species stochastic chemostat model. In this model, we assume that the nutrient input concentration and the nutrition con-version rate are influenced by white noises. The global existence and uniqueness of the positive solution of the system are proved by using stochastic comparison theorem. By constructing stochastic Lyapunov function, using Ito formula and stochastic stability theory of stochastic differential equation, we show the persistence of the system and the extinction of the microor-ganism. Finally, numerical simulations are carried out to illustrate the theoretical results.In Chapter 3, We formulate a stochastic chemostat model with a non-monotone response function, and assume that the nutrient input concentration and the death rate are influenced by white noises. By using the stochastic comparison theorem, we first show that this model has a unique global positive solution. Through constructing stochastic Lyapunov functions we discuss how the solutions of stochastic model spiral around the corresponding equilibriums of the deterministic model when the noise intensity is less than some values, and the microorganism will be washed out when the noise intensity is large. Furthermore, we investigate that there exists a stationary distribution for this system. Finally, numerical simulations are presented to illustrate our mathematical findings.