Hopf Bifurcation Analysis for the Model of the Chemostat with One Species of Organism. (17th April 2013)

• Record Type: Journal Article
• Authors: Bai, Haiyun; Zhai, Yanhui
• Other Names: Rhandi Abdelaziz Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2013(2013)
• Publication Date: 2013-04-17
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2013/829045
• Languages: English
• ISSNs: 1085-3375

Abstract

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.