- About this Journal ·
- Abstracting and Indexing ·
- Advance Access ·
- 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
Journal of Applied Mathematics
Volume 2012 (2012), Article ID 768364, 15 pages
Hopf Bifurcation of a Differential-Algebraic Bioeconomic Model with Time Delay
1Jiangsu Key Laboratory for NSLSCS, Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China
2School of Science, Nantong University, Nantong 226008, China
Received 7 September 2012; Accepted 26 September 2012
Academic Editor: Junjie Wei
Copyright © 2012 Xiaojian Zhou 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.
- R. M. May, “Time delay versus stability in population models with two and three trophic levels,” Ecology, vol. 4, pp. 315–325, 1973.
- Y. Song and J. Wei, “Local Hopf bifurcation and global periodic solutions in a delayed predator-prey system,” Journal of Mathematical Analysis and Applications, vol. 301, no. 1, pp. 1–21, 2005.
- B. D. Hassard, N. D. Kazarinoff, and Y. H. Wan, Theory and Applications of Hopf Bifurcation, vol. 41, Cambridge University Press, Cambridge, UK, 1981.
- X.-P. Yan and W.-T. Li, “Hopf bifurcation and global periodic solutions in a delayed predator-prey system,” Applied Mathematics and Computation, vol. 177, no. 1, pp. 427–445, 2006.
- J. Wu, “Symmetric functional-differential equations and neural networks with memory,” Transactions of the American Mathematical Society, vol. 350, no. 12, pp. 4799–4838, 1998.
- S. Yuan and F. Zhang, “Stability and global Hopf bifurcation in a delayed predator-prey system,” Nonlinear Analysis, vol. 11, no. 2, pp. 959–977, 2010.
- H. S. Gordon, “The economic theory of a common property resource, the fishery,” Journal of Political Economy, vol. 62, pp. 124–142, 1954.
- Y. Zhang and Q. L. Zhang, “Chaotic control based on descriptor bioeconomic systems,” Control and Decision, vol. 22, pp. 445–452, 2007.
- Y. Zhang, Q. L. Zhang, and L. C. Zhao, “Bifurcations and control in singular biological economical model with stage structure,” Journal of Systems Engineering, vol. 22, pp. 232–238, 2007.
- X. Zhang, Q.-L. Zhang, C. Liu, and Z.-Y. Xiang, “Bifurcations of a singular prey-predator economic model with time delay and stage structure,” Chaos, Solitons and Fractals, vol. 42, no. 3, pp. 1485–1494, 2009.
- C. Liu, Q. Zhang, and X. Duan, “Dynamical behavior in a harvested differential-algebraic prey-predator model with discrete time delay and stage structure,” Journal of the Franklin Institute. Engineering and Applied Mathematics, vol. 346, no. 10, pp. 1038–1059, 2009.
- C. Liu, Q. Zhang, X. Zhang, and X. Duan, “Dynamical behavior in a stage-structured differential-algebraic prey-predator model with discrete time delay and harvesting,” Journal of Computational and Applied Mathematics, vol. 231, no. 2, pp. 612–625, 2009.
- Y. Feng, Q. Zhang, and C. Liu, “Dynamical behavior in a harvested differential-algebraic allelopathic phytoplankton model,” International Journal of Information & Systems Sciences, vol. 5, no. 3-4, pp. 558–571, 2009.
- Q. Zhang, C. Liu, and X. Zhang, Complexity, Analysis and Control of Singular Bio-logical Systems, Springer, 2012.
- G. Zhang, L. Zhu, and B. Chen, “Hopf bifurcation in a delayed differential-algebraic biological economic system,” Nonlinear Analysis, vol. 12, no. 3, pp. 1708–1719, 2011.
- B. S. Chen, X. X. Liao, and Y. Q. Liu, “Normal forms and bifurcations for differential-algebraic systems,” Acta Mathematicae Applicatae Sinica, vol. 23, no. 3, pp. 429–443, 2000 (Chinese).
- K. L. Cooke and Z. Grossman, “Discrete delay, distributed delay and stability switches,” Journal of Mathematical Analysis and Applications, vol. 86, no. 2, pp. 592–627, 1982.
- Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, vol. 191 of Mathematics in Science and Engineering, Academic Press, Boston, Mass, USA, 1993.
- S. Ruan, “Absolute stability, conditional stability and bifurcation in Kolmogorov-type predator-prey systems with discrete delays,” Quarterly of Applied Mathematics, vol. 59, no. 1, pp. 159–173, 2001.
- J. Wei and S. Ruan, “Stability and bifurcation in a neural network model with two delays,” Physica D, vol. 130, no. 3-4, pp. 255–272, 1999.