Dynamic Analysis Of Two Impulsive Stochastic Nonautonomous Chemostat Models In Polluted Environment

Based on the knowledge of biological mathematical model and stochastic differential equations,the dynamics of two non-autonomous chemostat models with impulse effect and random disturbance in polluted environment are analyzed in this paper.One is the chemostat model with saturation growth rate and bilinear growth rate.The conditions for microbial extinction and persistence are analyzed.The other is the trophic cascade chemostat model with nonlinear perturbation.The dynamic behaviors of the stochastic system with white noises and regime switching are discussed respectively.Chapter 1 briefly introduces the research background and practical significance of the chemostat model,and gives some basic definitions and lemmas of stochastic differential equation and impulsive differential equation,and explains the main work and innovation of the whole paper.In Chapter 2,a novel impulsive stochastic nonautonomous chemostat model with the saturated and bilinear growth rates in a polluted environment is presented.By using the theory of impulsive differential equation and Lyapunov function,the threshold for the extinction and persistence of microorganisms is obtained,and then it is proved that the stochastic periodic system has at least one nontrivial positive periodic solution.The results show that different levels of pulse toxin input and random noise have different effects on the survival and extinction of microorganisms.Finally,a series of numerical simulations are used to verify the rationality of the theoretical results.In Chapter 3,the stochastic dynamics of the trophic cascade chemostat model disturbed by regime switching,nonlinear perturbation and pulse toxin input is studied.For stochastic system with only white noise interference,sufficient conditions for stochastical ultimate boundedness and stochastical permanence are obtained,and it is demonstrated that the stochastic system has at least one nontrivial positive periodic solution.For the system with Markov regime switching,sufficient conditions for extinction of the microorganisms are established.Then it is proved that the system is ergodic and has a stationary distribution.The results show that both pulse toxin input and random noise have great influence on the survival and extinction of microorganisms in this two systems.Finally,some examples and numerical simulations are given to illustrate the results of the theoretical analysis.Chapter 4 summarizes the main contents of the research,analyzes the biological significance of the corresponding conclusions,and makes the prospect of the future work.