Chemostat Model With Growth Delay And Impulsive Effects

In this paper, we mainly discuss two kinds of Chemostat model, competition and predation. By the theory on impulsive delay differential equation, we separately study the conditions of these systems about persistence and extinction. The article includes three chapters.In chapter 1, we introduce the research background of this article, the main task and some important preliminaries.In chapter 2, we mainly study two Chemostat models under different cases. In first part, we establish a three-dimensional competition model with variable consumption and injecting nutrition in pulse. By using techniques of comparison, small-amplitude perturbation skills and Floquet theorem, we study the system on persistence and extinction in the model. In next part, we consider a producing toxin model, with impulsive nutrition and toxin. In addition to this, we add growth delay causing by metabolism to the model. By constructingâ…¤function, we obtain any solution of the system is bounded, further, we also get the sufficient condition of sustainability and extinction of the system.In chapter 3, we discuss a Chemostat model with single-nutrient food chain. In this paper, we develop the absorption function,and introduce growth delay, so we construct a single-nutrient food chain model with delay and many population. By constructingâ…¤function, the model is proved dissipative.Futher, by comparison theorem for delay differential equations and mathe-matical foundation analysis, we study whether the system is uniformly persistent, last we gain the sufficient condition oflasting existence.