Analysis Of A Delayed Chemostat Model

Continuous cultivation of cells is the core of the modern biotechnology industry,and the vessel of continuous cell culture:chemostat gets more and more people’s attention. In recently years, people have done a lot of scientific researches about the chemostat model widely. In this paper, we establish two chemostat models with time delay and use the basic principle of differential equation, Characteristic root method and the method of Lyapunov function to analyze the models. This paper is divided into four chapters.In the first chapter, we introduce the studying background and significance of chemo-stat and summarize the progress of chemostat model, especially the chemostat model with time delay. and give a foreshadowing about the involved main theoretical basic knowledge in this paper.In the second chapter, we replace a generalized functional response in classical chemostat model. Firstly, we prove that the solutions of the model are positive and bounded by using the basic differential theories of equations. Secondly. we calculate the basic reproduction number of the system and analyze the existence conditions of equilib-ria. Moreover, we use the theory of characteristic roots to study local asymptotic stability of equilibria. Finally, we study global asymptotically stability of bacteria extinction e-quilibrium and the infection-free equilibrium by constructing Lyapunov functions.In the third chapter, combining with the biological significance of the model, we change the delay of the previous model to distributed delays, making it more realistic. and using the second chapter of the similar methods.In the last chapter, depending on the existing model, we analyze the improved points of the model and put forward the direction of further research, based on the analysis of the biological significance of a number of variables in the model.