Dynamical Behaviors Study Of Chemostat Model With Impulsive Input

In the research of microorganism, Using of chemostat to the development microor-ganism is an important research means, By the mathematics model of setting up the mi-croorganism growth regulation, announce to public the microorganism kinds growth anddecay political reform trend, so the studying of chemostat model has important ecosystemmeaning. The microorganism model (Chemostat model) of the dynamics behavior werestudied by many researcher, many good results of the permanence, the extinction, theglobally attractive of chemostat system were obtained. In this paper, we mainly discussthe chemostat model with nutrient recycling and impulsive input, the chemostat modelwith impulsive input delayed response and nutrient recycling in a polluted environment,the chemostat model impulsive di?usion on nutrients in a polluted environment. By usingthe comparison theorem of impulsive di?erential equation mainly, the su?cient conditionsof the permanence and the extinction of system are obtained, respectively.The main contents in this paper can be summarized as follows:In section 1, we present research background, purpose and significance of the chemo-stat model, and then the research status and results of the chemostat model are given.Finally the organization of this paper is also presented.In Section 2, the two species chemostat model with nutrient recycling and impulsiveinput is studied, and the preliminary information is given, by the comparison theoremof impulsive di?erential equation, the permanence and the extinction of the system aregiven. Finally, the numerical simulation is given. By the numerical simulation, the systemis also globally attractive.In Section 3, the delay chemostat model with impulsive input and nutrient recyclingin a polluted environment is studied, and the preliminary information is given, by thecomparison theorem of impulsive di?erential equation, the permanence and the extinctionof the system are given. Finally, the numerical simulation is given. By the numerical simulation, the system is also globally attractive.In Section 4, the delay chemostat model impulsive di?usion on nutrients is consid-ered, and the preliminary information is given, by the stroboscopic map, we obtain amicroorganism-extinction periodic solution. The permanent condition of the investigatedsystem is also obtained by the theory on impulsive delay di?erential equation. Finally, thenumerical simulation is given. By the numerical simulation, the system is also globallyattractive...