Study Of Chemostat Model With Impulsive Effect And Harvest

Chemostat is a main experimental apparatus for microbial cultivation.By establish-ing microbial cultivation model shows the dynamic behavior of system with persistence,extinguishing and balance the existence and so on.Besides,it provides the theoretical basis and scientific guidance for us to culture beneficial microorganisms and eliminate harmful microorganisms.In addition,the waters of plankton are the bottom of the food chain,the research on plankton Chemostat model has important ecological signifi-cance.In recent years,the dynamic behaviors of chemostat model have been discussed by many authors,such as persistence,globally attractive and the existence of the equilib-rium point of dynamic behavior,and so on.Under the inspiration of these models,this article discussed in the following three aspects:the first paper is on a chemostat model with nutrient recycling and harvest with impulsive effect,the second paper is dynamic behaviors of chemostat model with delayed growth response and harvest with impulsive effect,the third paper is on a plankton-nutrient chemostat model with hibernation and time delay.We use the main theorem of impulsive differential equation and possess the sufficient conditions about persistence and extinction for the above system.The main contents of this paper can be summarized as follows:In section 1,we introduce the research background,purpose and significance of the microbial growth model,and present the current research situation and results of chemo-stat model with impulsive effect.The structure of this article is also showed in the last part.In section 2,we quote some basic lemmas and give the process of proof in this paper.In section 3,we mainly study a chemostat model with nutrient recycling and har-vest with impulsive effect,by using the comparison theorem of impulsive differential e-quation and Floquet theory,the sufficient conditions on the global attractivity of the microorganism-free periodic solution and the permanence of the system are estimated.Finally we verify the accuracy of theory by numerical simulation.In section 4,we give the threshold of dynamic behaviors of chemostat model with delayed growth response and harvest with impulsive effect,and make full use of the threshold to prove the permanence and the extinction of the system.In order to illustrate the effectiveness of our theories,we shall present two examples in the last section.In section 5,we discussed the permanence and the extinction of a plankton-nutrient chemostat model with hibernation and time delay.In the case of pulse disturbance,time delay has an important effect on the system.