Study Of Chemostat Model With Nutrient Recycling And Impulsive Effects

The chemostat is a important laboratory apparatus to study the growth of microor-ganisms in a continuous cultured environment. It has the advantage of being easilyimplementable in a laboratory and hence the model has been subject to extensive testsand experiments. In addition, Chemostat model can simulate many natural phenomena ,such as the growth of single-celled algae phytoplankton in Lakes and oceans. The researchcontent mainly includes permanence, extinction, local or global attractive, periodicity andoscillation and so on. These research is useful for our work of Microorganism training.In this paper, the chemostat model with nutrient recycling and impulsive input and in-hibitor and the chemostat model with impulsive state feedback control model are studied.The major methods adopted are the comparison theorem of impulsive di?erential equa-tion mainly and the existence criteria of periodic solution of a general planar impulsiveautonomous system etc.The main contents in this paper can be summarized as follows:The first section is introduction, in which we present research background and signif-icance of the chemostat model, and then the research status and results of the chemostatmodel are given. Finally the organization of this paper is also presented.In Section 2, the chemostat model with impulsive input and nutrient recycling andone inhibitor is studied. At first the preliminary information is given, we will get theboundedness of solution by the Liapunov function, and then 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 chemostat model with impulsive state feedback control is studied.At first, We obtain su?cient conditions of the global asymptotical stability of the systemwithout impulsive state feedback control. Furthermore, By the existence criteria of pe- riodic solution of a general planar impulsive autonomous system, the conditions for theexistence of an order one periodic solution is gotten as well. Finally, some discussions andnumerical simulations are given.