The Unstirred Chemostat Model With Internal Storage And Toxin Morality:Steady State Analysis

In this thesis, we study the existence of steady-state solutions which arise from a mathematical model of two microbial populations competing for a single-limiting nutrient with internal storage and toxin mortality in an unstirred chemostat. This thesis is divided into three chapters.The first chapter mainly introduces the background of chemostat. We show the significance of the research chemostat and then discuss the current research situation, based on which we put forward the problem of this thesis.The second chapter briefly describes the main knowledge and methods prepared for this paper and studies the equation arising from internal storage structure and toxins produced by single population model. Using the global bifurcation theory, we give the sufficient conditions for the existence of its steady-state solution.The third chapter considers two species compete for a limiting nutrient. We first presented the stability of the two semi-trivial solutions when one species does not exist. Then using the global bifurcation theory, we give the conditions for the existence of steady state solutions of two populations.