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Abstract and Applied Analysis
Volume 2010, Article ID 156725, 18 pages
http://dx.doi.org/10.1155/2010/156725
Research Article

Global Stability and Oscillation of a Discrete Annual Plants Model

1Department of Mathematics, College of Science, King Saud University, Riyadh 11451, Saudi Arabia
2Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

Received 26 September 2010; Accepted 2 November 2010

Academic Editor: Nicholas Alikakos

Copyright © 2010 S. H. Saker. 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,” Journal of Animal Ecology, vol. 44, pp. 283–296, 1975. View at Google Scholar
  2. P. Cull, “Local and global stability for population models,” Biological Cybernetics, vol. 54, no. 3, pp. 141–149, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. P. Cull, “Global stability of population models,” Bulletin of Mathematical Biology, vol. 43, no. 1, pp. 47–58, 1981. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. P. Cull, “Stability of discrete one-dimensional population models,” Bulletin of Mathematical Biology, vol. 50, no. 1, pp. 67–75, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. P. Cull, “Stability in one-dimensional models,” Scientiae Mathematicae Japonicae, vol. 58, no. 2, pp. 367–375, 2003. View at Google Scholar · View at Zentralblatt MATH
  6. P. Cull, “Population models: stability in one dimension,” Bulletin of Mathematical Biology, vol. 69, no. 3, pp. 989–1017, 2007. View at Publisher · View at Google Scholar
  7. E. Braverman and S. H. Saker, “Permanence, oscillation and attractivity of the discrete hematopoiesis model with variable coefficients,” Nonlinear Analysis: Theory, Methods & Applications, vol. 67, no. 10, pp. 2955–2965, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. E. Braverman and S. H. Saker, “On the Cushing-Henson conjecture, delay difference equations and attenuant cycles,” Journal of Difference Equations and Applications, vol. 14, no. 3, pp. 275–286, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. E. M. Elabbasy and S. H. Saker, “Periodic solutions and oscillation of discrete non-linear delay population dynamics model with external force,” IMA Journal of Applied Mathematics, vol. 70, no. 6, pp. 753–767, 2005. View at Publisher · View at Google Scholar
  10. A. F. Ivanov, “On global stability in a nonlinear discrete model,” Nonlinear Analysis: Theory, Methods & Applications, vol. 23, no. 11, pp. 1383–1389, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. V. L. Kocić and G. Ladas, Global Behavior of Nonlinear Difference Equations of Higher Order with Applications, vol. 256 of Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1993.
  12. R. M. May, “Biological populations with nonoverlapping generations: stable points, stable cycles, and chaos,” Science, vol. 186, no. 4164, pp. 645–647, 1974. View at Google Scholar
  13. R. M. May, “Simple mathematical models with very complicated dynamics,” Nature, vol. 261, pp. 459–467, 1976. View at Google Scholar
  14. R. M. May, “Nonlinear problems in ecology and resources management,” in Chaotic Behaviour of Deterministic Systems, G. Toos, R. H. G. Helleman, and R. Stora, Eds., North-Holand, 1983. View at Google Scholar
  15. S. H. Saker, “Qualitative analysis of discrete nonlinear delay survival red blood cells model,” Nonlinear Analysis: Real World Applications, vol. 9, no. 2, pp. 471–489, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. S. H. Saker, “Periodic solutions, oscillation and attractivity of discrete nonlinear delay population model,” Mathematical and Computer Modelling, vol. 47, no. 3-4, pp. 278–297, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. H. R. Thieme, Mathematics in Population Biology, Princeton Series in Theoretical and Computational Biology, Princeton University Press, Princeton, NJ, USA, 2003.
  18. A. R. Watkinson, “Density-dependence in single-species populations of plants,” Journal of Theoretical Biology, vol. 83, no. 2, pp. 345–357, 1980. View at Google Scholar
  19. V. L. Kocić and G. Ladas, “Global attractivity in a second-order nonlinear difference equation,” Journal of Mathematical Analysis and Applications, vol. 180, no. 1, pp. 144–150, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  20. E. C. Pielou, Population and Community Ecology, Gordon and Breach, New York, NY, USA, 1974.
  21. I. Győri and M. Pituk, “Asymptotic stability in a linear delay difference equation,” pp. 295–299, Gordon and Breach. View at Google Scholar
  22. L. H. Erbe, H. Xia, and J. S. Yu, “Global stability of a linear nonautonomous delay difference equation,” Journal of Difference Equations and Applications, vol. 1, no. 2, pp. 151–161, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  23. I. Kovácsvölgyi, “The asymptotic stability of difference equations,” Applied Mathematics Letters, vol. 13, no. 1, pp. 1–6, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  24. J. S. Yu and S. S. Cheng, “A stability criterion for a neutral difference equation with delay,” Applied Mathematics Letters, vol. 7, no. 6, pp. 75–80, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  25. 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
  26. G. Ladas, Ch. G. Philos, and Y. G. Sficas, “Sharp conditions for the oscillation of delay difference equations,” Journal of Applied Mathematics and Simulation, vol. 2, no. 2, pp. 101–111, 1989. View at Google Scholar · View at Zentralblatt MATH
  27. S. A. Kuruklis and G. Ladas, “Oscillations and global attractivity in a discrete delay logistic model,” Quarterly of Applied Mathematics, vol. 50, no. 2, pp. 227–233, 1992. View at Google Scholar · View at Zentralblatt MATH