Discrete Dynamics in Nature and Society 
Volume 2007 (2007), Article ID 90158, 12 pages
doi:10.1155/2007/90158
Research Article

On the Study of Chemostat Model with Pulsed Input in a Polluted Environment

Zhong Zhao1 and Xinyu Song2

 1Department of Mathematics, Huanghuai University, Henan 463000, Zhumadian, China
2Department of Mathematics, Xinyang Normal University, Henan 464000, Xinyang, China
Received 14 August 2006; Revised 8 December 2006; Accepted 1 January 2007

Abstract

Chemostat model with pulsed input in a polluted environment is considered. By using the Floquet theorem, we find that the microorganism eradication periodic solution is globally asymptotically stable if the impulsive period T is more than a critical value. At the same time, we can find that the nutrient and microorganism are permanent if the impulsive period T is less than the critical value.