- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 829045, 7 pages
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.
- X. Li, J. Pan, and Q. Huang, “Hopf bifurcation analysis of some modified chemostat models,” Northeastern Mathematical Journal, vol. 14, no. 4, pp. 392–400, 1998.
- X.-y. Li, M.-h. Qian, J.-p. Yang, and Q.-C. Huang, “Hopf bifurcations of a chemostat system with bi-parameters,” Northeastern Mathematical Journal, vol. 20, no. 2, pp. 167–174, 2004.
- H. I. Freedman, J. W.-H. So, and P. Waltman, “Coexistence in a model of competition in the chemostat incorporating discrete delays,” SIAM Journal on Applied Mathematics, vol. 49, no. 3, pp. 859–870, 1989.
- J. Hale, Theory of Functional Differential Equations, Springer, 1977.
- J. K. Hale and S. M. V. Lunel, Introduction to Functional Differential Equations, Springer, 1995.
- G. Mircea, M. Neamtu, and D. Opris, Dynamical Systems from Economy, Mechanic and Biology Described by Differential Equations with Time Delay, Mirton, 2003.
- J. Wei and C. Yu, “Hopf bifurcation analysis in a model of oscillatory gene expression with delay,” Proceedings of the Royal Society of Edinburgh A, vol. 139, no. 4, pp. 879–895, 2009.
- N. A. M. Monk, “Oscillatory expression of Hes1, p53, and NF-κB driven by transcriptional time delays,” Current Biology, vol. 13, no. 16, pp. 1409–1413, 2003.
- Y. Song and J. Wei, “Bifurcation analysis for Chen's system with delayed feedback and its application to control of chaos,” Chaos, Solitons & Fractals, vol. 22, no. 1, pp. 75–91, 2004.
- Y. Song, J. Wei, and M. Han, “Local and global Hopf bifurcation in a delayed hematopoiesis model,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 14, no. 11, pp. 3909–3919, 2004.
- S. Ruan and J. Wei, “On the zeros of transcendental functions with applications to stability of delay differential equations with two delays,” Dynamics of Continuous, Discrete & Impulsive Systems A, vol. 10, no. 6, pp. 863–874, 2003.
- J. Wei, “Bifurcation analysis in a scalar delay differential equation,” Nonlinearity, vol. 20, no. 11, pp. 2483–2498, 2007.