- 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
Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 724325, 10 pages
Global Dynamics of a Predator-Prey Model with Stage Structure and Delayed Predator Response
Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, No. 97 Heping West Road, Shijiazhuang, Hebei 050003, China
Received 21 May 2013; Accepted 27 October 2013
Academic Editor: Qi-Ru Wang
Copyright © 2013 Lili Wang and Rui Xu. 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.
- S. Zhang, D. Tan, and L. Chen, “Chaos in periodically forced Holling type II predator-prey system with impulsive perturbations,” Chaos, Solitons and Fractals, vol. 28, no. 2, pp. 367–376, 2006.
- C. S. Holling, “The functional response of predator to prey density and its role in mimicry and population regulation,” Memoirs of the Entomological Society of Canada, vol. 45, pp. 1–60, 1965.
- R. Xu, M. A. J. Chaplain, and F. A. Davidson, “Periodic solutions for a predator-prey model with Holling-type functional response and time delays,” Applied Mathematics and Computation, vol. 161, no. 2, pp. 637–654, 2005.
- W. Ko and K. Ryu, “Qualitative analysis of a predator-prey model with Holling type II functional response incorporating a prey refuge,” Journal of Differential Equations, vol. 231, no. 2, pp. 534–550, 2006.
- K. Gopalsamy, Stability and Oscillations in Delay Differential Equations of Population Dynamics, Kluwer Academic, Dordrecht, The Netherlands, 1992.
- Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, Boston, Mass, USA, 1993.
- P. J. Wangersky and W. J. Cunningham, “Time lag in prey-predator population models,” Ecology, vol. 38, pp. 136–139, 1957.
- W. Wang, “Global dynamics of a population model with stage structure for predator,” in Advanced Topics in Biomathematics: Proceeding of the International Conference on Mathematical Biology, L. Chen, S. Ruan, and J. Zhu, Eds., pp. 253–257, World Scientific, Singapore, 1997.
- P. Georgescu and Y.-H. Hsieh, “Global dynamics of a predator-prey model with stage structure for the predator,” SIAM Journal on Applied Mathematics, vol. 67, no. 5, pp. 1379–1395, 2007.
- X. Tian and R. Xu, “Global dynamics of a predator-prey system with Holling type II functional response,” Nonlinear Analysis: Modelling and Control, vol. 16, no. 2, pp. 242–253, 2011.
- J. K. Hale, Theory of Functional Differential Equations, Springer, New York, NY, USA, 1976.
- S. Ruan and J. Wei, “On the zeros of a third degree exponential polynomial with applications to a delayed model for the control of testosterone secretion,” IMA Journal of Mathemathics Applied in Medicine and Biology, vol. 18, no. 1, pp. 41–52, 2001.
- J. K. Hale and P. Waltman, “Persistence in infinite-dimensional systems,” SIAM Journal on Mathematical Analysis, vol. 20, no. 2, pp. 388–395, 1989.
- H. L. Smith, “Monotone semiflows generated by functional-differential equations,” Journal of Differential Equations, vol. 66, no. 3, pp. 420–442, 1987.