Study Of Chemostat Model On Two Substrates

Chemostat model represents a basic model of a open system in microbial ecology.It plays an important role as a model in mathematical biology. By studying of thepermanence, the extinction and the globally attractivity of the equilibrium and so on,can the microorganisms in nature went on by men's control, so the studying of chemostatmodel has important academic meaning and actual meaning. In this paper, the delayedchemostat model with impulsive input and the delayed chemostat model with impulsiveinput in a polluted environment on two substrates are studied mainly. By using thecomparison theorem of impulsive di?erential equation mainly, the su?cient conditions ofthe permanence and the extinction of system are obtained respectively.The main contents in this paper can be summarized as follows:The first section is introduction, in which we present research background, purposeand significance of the chemostat model, and then the research status and results of thechemostat model are given. Finally the organization of this paper is also presented.In Section 2, the delayed chemostat model with impulsive input is studied on twosubstrates, and the preliminary information is given, by the comparison theorem of im-pulsive di?erential equation and Lemma 2.2, the permanence and the extinction of thesystem are given. Finally, the numerical simulation is given. By the numerical simulation,the system is also globally attractive.In Section 3, the delayed chemostat model with impulsive input is studied in a pol-luted environment on two substrates is studied, and the preliminary information is given,by the comparison theorem of impulsive di?erential equation and Lemma 2.2, the per-manence and the extinction of the system are given. Finally, the numerical simulation isgiven. By the numerical simulation, the system is also globally attractive.