The Dynamics Of A Food Chain Model In The Chemostat

In this paper, we mainly summarize and analyse food chain model in the chemostat. Thearticle includes three chapters.In chapter 1, we introduce the research background of this article and the main task.In chapter 2, we summarize research status of food chain model in the chemostat. Diferenttypes of equations including ordinary diferential equations, impulsive diferential equations anddelay diferential equations have been used to model chemostat. Topics cover stability of solu-tions, persistence of systems, existence of periodic solutions, and system complexities includingbifurcation and chaos.In chapter 3, we study of a Crowley-Martin type food chain chemostat. At frst, we ob-tain the local stability conditions for the equilibrium point, by using the qualitative theory ofdiferential equation; Next, By constructing V function,we prove the global stability of the pos-itive equilibrium point, further, the system is studied to obtain the sufcient condition for thepermanence. Finally, existence of limit cycles are obtained by numerical simulation.