The Study On Chemostat Model With Plasmid Or External Inhibitor

The chemostat is an organism of experimental device of artificial cultivation, is used to provide a controlled environment, can grow in nutrient limited conditions of microbial population in this environment. This paper develops and studies two kinds of having an external inhibitor chemostat competition model, using the Lyapunov function and the La Salle invariant principle of dynamics system. The thesis contains a total of four chapters.The first chapter introduces the basic constant theoretical knowledge of device, and described with external inhibitor chemostat competition model, discussed the current situation of research at home and abroad.The second chapter introduces some basic theorems needed in this paperThe third chapter in the chemostat model discussed by external inhibitor and plasmid, which the inhibitors only for microbial1 x inhibition and lethal, microorganisms2 x are plasmid load, but the plasmid may be in the process of reproduction will be lost, leading to those not containing plasmid. Loss of plasmid transformation into microbial1 x.The two part is microbial microbial yield constant is the same, because they have the same organism, the difference is containing and not containing plasmid. The analysis of the development of this model and discuss the existence and stability of the equilibria.The fourth chapter considers the chemostat competition model with external inhibitors. The introduction of this inhibitor to a competitor deadly effects and inhibit their growth, but this kind of inhibitor can be another competitor absorption without affecting its growth. In order to get the existence and stability of this kind of model boundary equilibrium is mainly to the discussion by Lyapunov function. Necessary and sufficient conditions for the existence of the internal equilibrium point is given. By numerical simulation, if the existence of internal equilibrium, then the system may be globally stable or a stable limit cycle.