Discrete Dynamics in Nature and Society
Volume 2010 (2010), Article ID 830951, 21 pages
doi:10.1155/2010/830951
Research Article

Global Behaviors of a Chemostat Model with Delayed Nutrient Recycling and Periodically Pulsed Input

Kai Wang,1 Zhidong Teng,1 and Fengqin Zhang2

1College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China
2Department of Mathematics, Yuncheng University, Yuncheng 044000, China

Received 27 July 2010; Accepted 20 September 2010

Academic Editor: Antonia Vecchio

Copyright © 2010 Kai Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The dynamic behaviors in a chemostat model with delayed nutrient recycling and periodically pulsed input are studied. By introducing new analysis technique, the sufficient and necessary conditions on the permanence and extinction of the microorganisms are obtained. Furthermore, by using the Liapunov function method, the sufficient condition on the global attractivity of the model is established. Finally, an example is given to demonstrate the effectiveness of the results in this paper.