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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 829045, 7 pages
http://dx.doi.org/10.1155/2013/829045
Research Article

Hopf Bifurcation Analysis for the Model of the Chemostat with One Species of Organism

School of Science, Tianjin Polytechnic University, Tianjin 300387, China

Received 19 November 2012; Revised 3 March 2013; Accepted 3 March 2013

Academic Editor: Abdelaziz Rhandi

Copyright © 2013 Haiyun Bai and Yanhui Zhai. 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

We research the dynamics of the chemostat model with time delay. The conclusion confirms that a Hopf bifurcation occurs due to the existence of stability switches when the delay varies. By using the normal form theory and center manifold method, we derive the explicit formulas determining the stability and direction of bifurcating periodic solutions. Finally, some numerical simulations are given to illustrate the effectiveness of our results.