Study On The Dynamics Of Two Classes Chemostat Models

In this paper, by using the theory of impulsive diferential equations and delay diferentialequations, we study two chemostat systems(two-nutrient chemostat model and nutrient chemo-stat model) . We main discuss the extinction of the micoorganisms and the permanence of thesesystems. The article is divided into three chapters.In Chapter 1, We introduce some knowledge of biology mathematics and the present situ-ation .In Chapter 2, we study a two-nutrient and one-microorganism delayed chemostat modelwith periodically pulsed input and polluted environment.Through the comparison theroem ofpulse equation, we show that there exists a microorganism-free periodic solution,which is globallyattractive.At the same time,we give the sufcient condition for the permanence of the modelwith time delay and pulsed input.In Chapter 3, we study chemostat model with an external inhibitor, nutrient recycling andperiodically pulsed input . Through the comparison theorem of pulse equation and Liapunovmethod,we get the sufcient and necessary conditions on the permanence and extinction of themicroorganism. Furthermore,by using the Liapunov function method,the sufcient condition onthe global attractivity of the system is established.