- 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
Abstract and Applied Analysis
Volume 2014 (2014), Article ID 624162, 12 pages
Stability and Hopf Bifurcation of Delayed Predator-Prey System Incorporating Harvesting
College of Mathematics and Computer Science, Fuzhou University, Fuzhou, Fujian 350116, China
Received 28 September 2013; Accepted 6 January 2014; Published 6 March 2014
Academic Editor: Chun-Lei Tang
Copyright © 2014 Fengying Wei 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.
- K. Gopalsamy, Stability and Oscillations in Delay Differential Equations of Population Dynamics, vol. 74 of Mathematics and its Applications, Kluwer Academic Publishers Group, Dordrecht, The Netherlands, 1992.
- D. Xiao and S. Ruan, “Multiple bifurcations in a delayed predator-prey system with nonmonotonic functional response,” Journal of Differential Equations, vol. 176, no. 2, pp. 494–510, 2001.
- J.-F. Zhang, “Bifurcation analysis of a modified Holling-Tanner predator-prey model with time delay,” Applied Mathematical Modelling, vol. 36, no. 3, pp. 1219–1231, 2012.
- S. Yuan and Y. Song, “Stability and Hopf bifurcations in a delayed Leslie-Gower predator-prey system,” Journal of Mathematical Analysis and Applications, vol. 355, no. 1, pp. 82–100, 2009.
- N. Bairagi and D. Jana, “On the stability and Hopf bifurcation of a delay-induced predator-prey system with habitat complexity,” Applied Mathematical Modelling, vol. 35, no. 7, pp. 3255–3267, 2011.
- C. Çelik, “The stability and Hopf bifurcation for a predator-prey system with time delay,” Chaos, Solitons and Fractals, vol. 37, no. 1, pp. 87–99, 2008.
- 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.
- R. M. May, “Time delay versus stability in population model with two or three trophic levels,” Ecology, vol. 54, pp. 315–325, 1973.
- T. K. Kar and A. Ghorai, “Dynamic behaviour of a delayed predator-prey model with harvesting,” Applied Mathematics and Computation, vol. 217, no. 22, pp. 9085–9104, 2011.
- S. B. Hsu and T. W. Huang, “Global stability for a class of predator-prey systems,” SIAM Journal on Applied Mathematics, vol. 55, no. 3, pp. 763–783, 1995.
- T. K. Kar, “Selective harvesting in a prey-predator fishery with time delay,” Mathematical and Computer Modelling, vol. 38, no. 3-4, pp. 449–458, 2003.
- B. D. Hassard, N. D. Kazarinoff, and Y. H. Wan, Theory and Applications of Hopf Bifurcation, vol. 41, Cambridge University Press, Cambridge, UK, 1981.
- K. Gopalsamy, “Harmless delays in model systems,” Bulletin of Mathematical Biology, vol. 45, no. 3, pp. 295–309, 1983.