Kinetic Behavior Of Two Classes Of Stochastic Chemostat Models

In this paper,we study the dynamical behaviors of two stochastic chemostat models with general growth response functions.The paper consists of four chapters.In chapter 1,we introduce the research background,main work,and related preliminary knowledge of this paper.In chapter 2,we study a class of stochastic chemostat model with general response functions.Firstly,we introduce the establishment of the model,and give the conditions that the general growth response functions satisfy.Secondly,we prove the existence and uniqueness of globally positive solutions of model by using Lyapunov function and It?o formula.Then,we further study the stochastic differential equations,and obtaine sufficient conditions for the extinction and persistence of microorganisms by using Strong law of large numbers and L'Hospital rule,ect.The main difficulty of the study is that there is no explicit expression of growth response functions,which brings difficulties to the construction of the Lyapunov function and qualitative analysis.Finally,through the numerical simulations,the theoretical results are verified.In chapter 3,we study the other stochastic chemostat model with general growth response functions.Firstly,we introduce the establishment of the model,and give the conditions that the general growth response functions satisfy,and we prove the existence and uniqueness of globally positive solutions of model by using Lyapunov function and It?o formula.Secondly,we study the properties of model solutions and sufficient conditions for the microbial extinction.Then,through specific examples,we analyse the existence of stationary distributions of the models.There is no explicit expression for the growth response functions,and there is no estimate of the uniform boundedness of the solutions in this kind of model,which is fundamentally different from the model studied in Chapter 2.Finally,the theoretical results are verified by numerical simulations.In chapter 4,we summarize the main findings and prospect the research work.