- 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 101649, 7 pages
A Global Attractor in Some Discrete Contest Competition Models with Delay under the Effect of Periodic Stocking
Department of Mathematics and Statistics, Sultan Qaboos University, P.O. Box 36 123, Al-Khod, Oman
Received 17 June 2013; Revised 3 September 2013; Accepted 16 September 2013
Academic Editor: Yanni Xiao
Copyright © 2013 Ziyad AlSharawi. 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.
- M. P. Hassell, “Density-dependence in single-species populations,” The Journal of Animal Ecology, vol. 44, pp. 283–295, 1975.
- M. Kot, Elements of Mathematical Ecology, Cambridge University Press, Cambridge, Uk, 2001.
- Å. Brännström and D. J. T. Sumpter, “The role of competition and clustering in population dynamics,” Proceedings of the Royal Society B, vol. 272, no. 1576, pp. 2065–2072, 2005.
- G. C. Varley, G. R. Gradwell, and M. P. Hassell, Insect Population Ecology, Blackwell Scientific, Oxford, UK, 1973.
- S. M. Henson and J. M. Gushing, “Hierarchical models of intra-specific competition: scramble versus contest,” Journal of Mathematical Biology, vol. 34, no. 7, pp. 755–772, 1996.
- R. Beverton and S. J. Holt, On the Dynamics of Exploited Fish Populations, The Blackburn Press, New Jersey, NJ, USA, 2004.
- S. A. Levin and R. M. May, “A note on difference-delay equations,” Theoretical Population Biology, vol. 9, no. 2, pp. 178–187, 1976.
- R. M. May, “Time-delay versus stability in population models with two and three trophic levels,” Ecology, vol. 54, pp. 315–325, 1973.
- L. Nunney, “Short time delays in population models: a role in enhancing stability,” Ecology, vol. 66, no. 6, pp. 1849–1858, 1985.
- C. E. Taylor and R. R. Sokal, “Oscillations in housefly population size due to time lags,” Ecology, vol. 57, pp. 1060–1067, 1976.
- V. L. Kocić and G. Ladas, Global Behavior of Nonlinear Difference Equations of Higher Order with Applications, vol. 256, Kluwer Academic, Dordrecht, The Netherlands, 1993.
- H. I. McCallum, “Effects of immigration on chaotic population dynamics,” Journal of Theoretical Biology, vol. 154, no. 3, pp. 277–284, 1992.
- G. D. Ruxton, “Low levels of immigration between chaotic populations can reduce system extinctions by inducing asynchronous regular cycles,” Proceedings of the Royal Society B, vol. 256, no. 1346, pp. 189–193, 1994.
- G. D. Ruxton, “The effect of emigration and immigration on the dynamics of a discrete-generation population,” Journal of Biosciences, vol. 20, no. 3, pp. 397–407, 1995.
- G. D. Ruxton and P. Rohani, “Population floors and the persistence of chaos in ecological models,” Theoretical Population Biology, vol. 53, no. 3, pp. 175–183, 1998.
- S. Sinha and P. K. Das, “Dynamics of simple one-dimensional maps under perturbation,” Pramana, vol. 48, no. 1, pp. 87–98, 1997.
- L. Stone, “Period-doubling reversals and chaos in simple ecological models,” Nature, vol. 365, no. 6447, pp. 617–620, 1993.
- L. Stone and D. Hart, “Effects of immigration on the dynamics of simple population models,” Theoretical Population Biology, vol. 55, no. 3, pp. 227–234, 1999.
- P. Sun and X. B. Yang, “Dynamic behaviors of the Ricker population model under a set of randomized perturbations,” Mathematical Biosciences, vol. 164, no. 2, pp. 147–159, 2000.
- R. Abu-Saris, Z. AlSharawi, and M. Rhouma, “The dynamics of some discrete models with delay under the effect of constant yield harvesting,” Chaos, Solitons & Fractals, vol. 54, pp. 26–38, 2013.
- G. Nyerges, “A note on a generalization of Pielou's equation,” Journal of Difference Equations and Applications, vol. 14, no. 5, pp. 563–565, 2008.
- E. Camouzis and G. Ladas, “Periodically forced Pielou's equation,” Journal of Mathematical Analysis and Applications, vol. 333, no. 1, pp. 117–127, 2007.
- E. Zeidler, Nonlinear Functional Analysis and Its Applications. I, Springer, New York, NY, USA, 1986.
- E. C. Pielou, Population and Community Ecology, Gordon and Breach, New York, NY, USA, 1974.