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Discrete Dynamics in Nature and Society
Volume 2006, Article ID 38310, 14 pages
http://dx.doi.org/10.1155/DDNS/2006/38310

Extinction and permanence of two-nutrient and one-microorganism chemostat model with pulsed input

1Department of Mathematics, Xinyang Normal University, Xinyang, Henan, Henan 464000, China
2Department of Mathematics, Huanghuai University, Xinyang, Zhumadian, Henan 463000, China

Received 9 November 2005; Accepted 27 February 2006

Copyright © 2006 Xinyu Song and Zhong Zhao. 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

A chemostat model with periodically pulsed input is considered. By using the Floquet theorem, we find that the microorganism eradication periodic solution (u1(t),v1(t),0) 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.