Study On Dynamical Behaviors Of Two Stochastic Chemostat Models With An Inhibitor

In this paper,we mainly study the dynamical behaviors of two stochastic chemostat models with an inhibitor.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,we consider a stochastic chemostat model with an inhibitor and noise in-dependent of population sizes.In the model,we assume that stochastic perturbations are of environment noise which are directly proportional to the concentration of the nutrient,inhibitor and the microorganisms.Firstly,the global existence and uniqueness of the positive solution of the model are proved by using stochastic Lyapunov function and Ito's formula.Then,because the equilibrium points of the deterministic chemostat model are not the equilibrium points of the stochastic chemostat model,so detailed analysis are discussed by reconstructing stochastic Lyapunov function and using Ito's formula,Gronwall inequality and strong law of large numbers.Furthermore,the steady state distributions are proved.Finally,numerical simulations are given to illustrate the correctness of the analytical results.In Chapter 3,we discuss another stochastic chemostat model with an inhibitor and s-tochastic environment noise disturbs the growth rates of the microorganisms.Firstly,the global existence and uniqueness of the positive solution of the model are proved by using stochastic Lyapunov function and Ito's formula.Then,because the washout equilibrium of the deter-ministic chemostat model are also the washout equilibrium of the stochastic chemostat model,so stochastic stability of the washout equilibrium of the stochastic chemostat model and the asymptotic behaviors are established by reconstructing stochastic Lyapunov function and using Ito's formula,and the theory of stochastic differential equation.At last,some simulations are given to illustrate the analytical results.