The Dynamics Of The Chemostat Competition Model

In this paper, we mainly summarize and study chemostat competition model, the article isdivided into three chapters.In chapter 1, we give some knowledge of biology mathematics , the introduction of chemo-stat model and some prelimineries.In chapter 2, we introduce the theory and results of chemostat competition model in recentyears. Diferent types of equations including ordinary diferential equations, impulsive diferen-tial equations and delay diferential equations have been used to model chemostat, the chemostatmodel with delay and impulsive efects. The research project involved include the stability of thesolution, the permanence of the system, the existence of periodic solution, competition exclusionprinciple, bifurcation problem etc.In chapter 3, we study a mode of a Crowley-Martin chemostat competition model withdelayed growth response and pulsed input concentration of the nutrient and inhibition. Byusing the comparsion theorem of the impulsive equations and the theory of delayed diferentialequations, we obtain the sufcient conditions for the global attractivity of the microorganism-extinction periodic solution and the permanence of the system.