Dynamic Analysis Of Two Kinds Of Chemostat Models With Impulsive Effects And Random Perturbation

Based on the knowledge of ordinary differential equations and stochastic biomathematical models,two types of chemostat models with impulsive effects and random disturbances are analyzed in the paper.One is a stochastic competitive chemostat model with saturated growth rate and impulsive toxin input.The persistence and extinction of deterministic system and stochastic system have been studied successively.The other is an impulsive stochastic chemostat model with nonlinear disturbances.Sufficient conditions for the extinction of microorganisms are found and the unique ergodic stationary distribution of the system is proved.Chapter 1 shows the research background of the subject,and introduces some basic definitions,basic theorems and inequalities related to the subject.Chapter 2 proposes a new stochastic competition chemostat model with saturated growth rate and impulsive toxicant input.The main purpose of this paper is to study the stochastic dynamics of a high-dimensional impulsive stochastic chemostat model and find the threshold between persistence and extinction for the impulsive stochastic chemostat system.Firstly,we investigate the stability of the periodic solution of the deterministic impulsive chemostat model and obtain the threshold between persistence and extinction for the system.Secondly,by using qualitative analysis method of impulsive stochastic differential equations,we obtain conditions for the extinction and persistence in mean of two microorganisms in the stochastic chemostat model.The results show that a stochastic disturbance or the impulsive effect can cause the extinction of microorganisms.Finally,we provide some examples together with numerical simulations to illustrate the analytical results and explain the biological implications.Chapter 3 investigates a new impulsive stochastic chemostat model with nonlinear perturbation in a polluted environment.We present the analysis and the criteria of the extinction of the microorganisms,and establish sufficient conditions for the existence of a unique ergodic stationary distribution of the model via Lyapunov functions method.The results show that both stochastic noise and impulsive toxicant input have great effects on the survival and extinction of the microorganisms.Moreover,we provide a series of numerical simulations to illustrate the analytical results.Chapter 4 summarizes the work of this article and makes the prospect of the future researches.