Study Of Chemostat Model With Impulsive Input And Nutrient Recycling

Chemostat model can simulate many phenomena in real life, so the studying ofchemostat model has important zoology meaning. By studying of the permanence, theextinction, the globally attractivity of system and the globally attractivity of the equi-librium and so on, can the microorganisms in nature went on by men's control, so thestudying of chemostat model has important academic meaning and actual meaning. Inthis paper, the chemostat model with nutrient recycling and impulsive input and thechemostat model with impulsive input and nutrient recycling in a polluted environmentare studied mainly. By using the comparison theorem of impulsive differential equationmainly, the sufficient conditions of the permanence and the extinction of system are ob-tained 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 Beddington-DeAngelis type chemostat model with nutrient recy-cling and impulsive input is studied, and the preliminary information is given, by thecomparison theorem of impulsive differential equation, the permanence and the extinc-tion of the system are given. Finally, the numerical simulation is given. By the numericalsimulation, the system is also globally attractive.In Section 3, the chemostat model with impulsive input and nutrient recycling in apolluted environment is studied, and the preliminary information is given, by the compar-ison theorem of impulsive differential equation, 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.