Research On Two Types Of Stochastic Chemostat Dynamical Models

The study of the chemostat model is essential for analyzing the evolution of natural ecosystems.Research scholars have achieved fruitful research results on deterministic chemostat models.However,in real ecosystems,the habitats of species are often disturbed by pollutants or toxins and environmental white noise.Therefore,when studying the chemostat model,considering random effect and pulse toxin input,the characteristics of microbial changes and development in the chemostat can be described more practically,which is beneficial to make reasonable prediction of microbial changes.In this paper,we first investigate a stochastic chemostat model with pulsed toxin input in a polluted environment,and then study a stochastic chemostat model with Monod-Haldane response function.The paper studies the dynamic behavior of these two types of stochastic chemostat models by using the theoretical knowledge of stochastic differential equations.In Chapter 1,We introduced the research background of the subject and some important basic theoretical knowledge.In Chapter 2,we propose a multi-nutrient and single microorganism chemostat model with stochastic effect and impulsive toxicant input.Firstly,for the system neglecting stochastic effect,we investigate the global dynamics including the existence and global asymptotic stability of 'microorganism-extinction' periodic solution,as well as the permanence of the system.Then,for the stochastic differential system with impulsive effect,we discuss the persistence and extinction of microorganisms with stochastic effect in a polluted environment.Our results indicate that the stochastic disturbance can lead to microbial extinction.Moreover,the concentration of toxicant will also affect the survival of microorganisms.Finally,our theoretical results are verified by numerical simulations.In Chapter 3,we formulate and investigate a two-microorganism and single nutrient chemostat model with Monod-Haldane response function and random perturbation.First,for the corresponding deterministic system,we introduce the conditions of the stability of the equilibrium points.Then,the existence and uniqueness of the global positive solution of the stochastic chemostat model are verified.Furthermore,we explore and obtain the criterions of the extinction and the permanence for the stochastic model.Finally,numerical simulations are introduced to illustrate our main results.In Chapter 4,we summarize the content of the full text,and look forward to the next research work.