A Kind Of Threshold Dynamics Of A Stochastic Chemostat Model With Nutrition Substitution

In this paper,a new type of stochastic chronostat model is established by introducing environmental white noise into a class of chemostat models with alternative nutrients.The qualitative analysis of the inequalities scaling technique is studied using the relevant theory and methods of differential equations.Its global dynamics.The research results of this paper provide a certain theoretical basis for the cultivation of alternative microorganisms.The full text is divided into five chapters.The first chapter introduces the research background of the topic,the related theoretical knowledge of differential equations and the main work of this paper.In the second chapter,firstly,the corresponding deterministic model system is obtained without considering the ambient white noise.Using the theory of ordinary differential equations,the stability of the equilibrium point of the model is studied,and the extinction and long-lasting thresholds of the microbial population are obtained.The influence of environmental white noise on microbial populations was mainly based on the theory,methods,and unequal scaling techniques of stochastic differential equations.The threshold dynamics of the model system under the condition of low ambient white noise intensity were discussed,and microorganisms were obtained.Extinction and average long-lasting conditions.Our results show that there is a large difference between the threshold of the random chemostat model and the threshold of the corresponding deterministic model.Large environmental noise will cause microbes to extinction,which is not conducive to the cultivation of microorganisms.Finally,the theoretical results obtained are verified by numerical simulation.The third chapter summarizes the full text and discusses the future research work.