Table of Contents Author Guidelines Submit a Manuscript
Discrete Dynamics in Nature and Society
Volume 2015, Article ID 160672, 11 pages
http://dx.doi.org/10.1155/2015/160672
Research Article

Basin of Attraction through Invariant Curves and Dominant Functions

1Department of Mathematics and Statistics, Sultan Qaboos University, P.O. Box 36, Alkhoud, 123 Muscat, Oman
2Sciences and Engineering, Paris-Sorbonne University Abu Dhabi, P.O. Box 38044, Abu Dhabi, UAE

Received 9 February 2015; Accepted 6 May 2015

Academic Editor: Garyfalos Papashinopoulos

Copyright © 2015 Ziyad AlSharawi 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.

Linked References

  1. V. L. Kocic and G. Ladas, Global Behavior of Nonlinear Difference Equations of Higher Order with Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1993.
  2. J. D. Murray, Mathematical Biology, Springer, New York, NY, USA, 1989.
  3. L. D. Mueller and A. Joshi, Stability in Model Populations, Princeton University Press, Princeton, NJ, USA, 2000.
  4. E. C. Pielou, Population and Community Ecology, Gordon and Breach, New York, NY, USA, 1974.
  5. 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 MathSciNet
  6. E. Liz, V. Tkachenko, and S. Trofimchuk, “Global stability in discrete population models with delayed-density dependence,” Mathematical Biosciences, vol. 199, no. 1, pp. 26–37, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. R. Abu-Saris, Z. AlSharawi, and M. B. 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. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. Z. AlSharawi, “A global attractor in some discrete contest competition models with delay under the effect of periodic stocking,” Abstract and Applied Analysis, vol. 2013, Article ID 101649, 7 pages, 2013. View at Publisher · View at Google Scholar
  9. Z. AlSharawi and M. B. Rhouma, “The Beverton-Holt model with periodic and conditional harvesting,” Journal of Biological Dynamics, vol. 3, no. 5, pp. 463–478, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  10. L. Arriola, “First integrals for difference equations,” Nonlinear Analysis: Theory, Methods & Applications, vol. 30, pp. 1191–1196, 1997. View at Google Scholar
  11. E. A. Grove and G. Ladas, Periodicities in Nonlinear Difference Equations, CRC Press, Boca Raton, Fla, USA, 2000.
  12. E. A. Grove, V. L. Kocic, and G. Ladas, “Classification of invariants for certain difference equations,” in Advances in Difference Equations: Proceedings of the Second International Conference on Difference Equations, Hungary, 1995, Gordon and Breach, 1997. View at Google Scholar
  13. T. Nesemann, “Invariants and Liapunov functions for nonautonomous systems,” Computers & Mathematics with Applications, vol. 42, no. 3–5, pp. 385–392, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. E. Camouzis and G. Ladas, Dynamics of Third-Order Rational Difference Equations with Open Problems and Conjectures, Chapman & Hall, CRC Press, 2008.
  15. R. D. Nussbaum, “Global stability, two conjectures and Maple,” Nonlinear Analysis: Theory, Methods & Applications, vol. 66, no. 5, pp. 1064–1090, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. P. Cull, “Enveloping implies global stability,” in Difference Equations and Discrete Dynamical Systems (Proceedings of the 9th Annual International Conference on Difference Equations and Applications, Los Angeles, Calif, USA, 2004), pp. 71–85, World Science Publisher, 2005. View at Google Scholar
  17. H. A. El-Morshedy and V. J. López, “Global attractors for difference equations dominated by one-dimensional maps,” Journal of Difference Equations and Applications, vol. 14, no. 4, pp. 391–410, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. V. J. Lopez, “The Y2K problem revisited,” Journal of Difference Equations and Applications, vol. 16, no. 1, pp. 105–119, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. O. Merino, “Global attractivity of the equilibrium of a difference equation: an elementary proof assisted by computer algebra system,” Journal of Difference Equations and Applications, vol. 17, no. 1, pp. 33–41, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  20. M. R. Kulenovic and G. Ladas, Dynamics of Second Order Rational Difference Equations, Chapman and Hall/CRC, Boca Raton, Fla, USA, 2002. View at MathSciNet