About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 101649, 7 pages
http://dx.doi.org/10.1155/2013/101649
Research Article

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.

Linked References

  1. M. P. Hassell, “Density-dependence in single-species populations,” The Journal of Animal Ecology, vol. 44, pp. 283–295, 1975.
  2. M. Kot, Elements of Mathematical Ecology, Cambridge University Press, Cambridge, Uk, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  3. 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. View at Publisher · View at Google Scholar · View at Scopus
  4. G. C. Varley, G. R. Gradwell, and M. P. Hassell, Insect Population Ecology, Blackwell Scientific, Oxford, UK, 1973.
  5. 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. View at Scopus
  6. R. Beverton and S. J. Holt, On the Dynamics of Exploited Fish Populations, The Blackburn Press, New Jersey, NJ, USA, 2004.
  7. S. A. Levin and R. M. May, “A note on difference-delay equations,” Theoretical Population Biology, vol. 9, no. 2, pp. 178–187, 1976. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. R. M. May, “Time-delay versus stability in population models with two and three trophic levels,” Ecology, vol. 54, pp. 315–325, 1973.
  9. L. Nunney, “Short time delays in population models: a role in enhancing stability,” Ecology, vol. 66, no. 6, pp. 1849–1858, 1985. View at Scopus
  10. C. E. Taylor and R. R. Sokal, “Oscillations in housefly population size due to time lags,” Ecology, vol. 57, pp. 1060–1067, 1976.
  11. 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. View at MathSciNet
  12. H. I. McCallum, “Effects of immigration on chaotic population dynamics,” Journal of Theoretical Biology, vol. 154, no. 3, pp. 277–284, 1992. View at Scopus
  13. 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. View at Publisher · View at Google Scholar · View at Scopus
  14. 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. View at Publisher · View at Google Scholar · View at Scopus
  15. 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. View at Publisher · View at Google Scholar · View at Scopus
  16. S. Sinha and P. K. Das, “Dynamics of simple one-dimensional maps under perturbation,” Pramana, vol. 48, no. 1, pp. 87–98, 1997. View at Scopus
  17. L. Stone, “Period-doubling reversals and chaos in simple ecological models,” Nature, vol. 365, no. 6447, pp. 617–620, 1993. View at Scopus
  18. 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. View at Publisher · View at Google Scholar · View at Scopus
  19. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. 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.
  21. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. E. Camouzis and G. Ladas, “Periodically forced Pielou's equation,” Journal of Mathematical Analysis and Applications, vol. 333, no. 1, pp. 117–127, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. E. Zeidler, Nonlinear Functional Analysis and Its Applications. I, Springer, New York, NY, USA, 1986. View at Publisher · View at Google Scholar · View at MathSciNet
  24. E. C. Pielou, Population and Community Ecology, Gordon and Breach, New York, NY, USA, 1974.