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Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 746738, 20 pages
http://dx.doi.org/10.1155/2012/746738
Research Article

Global Attractivity and Periodic Character of Difference Equation of Order Four

1Mathematics Department, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

Received 14 July 2012; Revised 2 September 2012; Accepted 17 September 2012

Academic Editor: Ibrahim Yalcinkaya

Copyright © 2012 M. A. Obaid 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. R. P. Agarwal and E. M. Elsayed, “On the solution of fourth-order rational recursive sequence,” Advanced Studies in Contemporary Mathematics, vol. 20, no. 4, pp. 525–545, 2010.
  2. E. M. Elabbasy, H. El-Metwally, and E. M. Elsayed, “Some properties and expressions of solutions for a class of nonlinear difference equation,” Utilitas Mathematica, vol. 87, pp. 93–110, 2012.
  3. E. M. Elabbasy, H. El-Metwally, and E. M. Elsayed, “On the difference equation xn+1=axn(bxn)/(cxndxn1),” Advances in Difference Equations, vol. 2006, Article ID 82579, 10 pages, 2006.
  4. E. M. Elabbasy, H. El-Metwally, and E. M. Elsayed, “Global behavior of the solutions of difference equation,” Advances in Difference Equations, vol. 2011, article 28, 2011.
  5. E. M. Elabbasy and E. M. Elsayed, “On the global attractivity of difference equation of higher order,” Carpathian Journal of Mathematics, vol. 24, no. 2, pp. 45–53, 2008.
  6. E. M. Elabbasy and E. M. Elsayed, “Global attractivity and periodic nature of a difference equation,” World Applied Sciences Journal, vol. 12, no. 1, pp. 39–47, 2011.
  7. E. M. Elsayed, “On the solution of some difference equations,” European Journal of Pure and Applied Mathematics, vol. 4, no. 3, pp. 287–303, 2011.
  8. E. M. Elsayed, “Dynamics of a recursive sequence of higher order,” Communications on Applied Nonlinear Analysis, vol. 16, no. 2, pp. 37–50, 2009.
  9. E. M. Elsayed, “Solution and attractivity for a rational recursive sequence,” Discrete Dynamics in Nature and Society, vol. 2011, Article ID 982309, 17 pages, 2011. View at Publisher · View at Google Scholar
  10. E. M. M. Elsayed, “Behavior of a rational recursive sequences,” Studia. Universitatis Babeş-Bolyai Mathematica, vol. 56, no. 1, pp. 27–42, 2011.
  11. E. M. Elsayed, “On the global attractivity and the solution of recursive sequence,” Studia Scientiarum Mathematicarum Hungarica, vol. 47, no. 3, pp. 401–418, 2010. View at Publisher · View at Google Scholar
  12. E. M. Elsayed, “On the dynamics of a higher-order rational recursive sequence,” Communications in Mathematical Analysis, vol. 12, no. 1, pp. 117–133, 2012.
  13. E. M. Elsayed, “Dynamics of recursive sequence of order two,” Kyungpook Mathematical Journal, vol. 50, no. 4, pp. 483–497, 2010. View at Publisher · View at Google Scholar
  14. E. M. Elsayed, “Solutions of rational difference systems of order two,” Mathematical and Computer Modelling, vol. 55, no. 3-4, pp. 378–384, 2012. View at Publisher · View at Google Scholar · View at Scopus
  15. E. A. Grove and G. Ladas, Periodicities in Nonlinear Difference Equations, vol. 4, Chapman & Hall/CRC, Boca Raton, Fla, USA, 2005.
  16. M. Saleh and M. Aloqeili, “On the rational difference equation xn+1=A+xn/xn-K,” Applied Mathematics and Computation, vol. 171, no. 2, pp. 862–869, 2005. View at Publisher · View at Google Scholar
  17. X. Yang, W. Su, B. Chen, G. M. Megson, and D. J. Evans, “On the recursive sequence xn+1=(axn1+bxn2)/(c+dxn1xn2),” Applied Mathematics and Computation, vol. 162, no. 3, pp. 1485–1497, 2005. View at Publisher · View at Google Scholar
  18. V. L. Kocić and G. Ladas, Global Behavior of Nonlinear Difference Equations of Higher Order with Applications, vol. 256, Kluwer Academic Publishers Group, Dordrecht, The Netherlands, 1993.
  19. M. R. S. Kulenović and G. Ladas, Dynamics of Second Order Rational Difference Equations With Open Problems and Conjectures, Chapman & Hall/CRC, Boca Raton, Fla, USA, 2002.
  20. T. Sun and H. Xi, “On convergence of the solutions of the difference equation xn+1=1+xn1/xn,” Journal of Mathematical Analysis and Applications, vol. 325, no. 2, pp. 1491–1494, 2007. View at Publisher · View at Google Scholar
  21. N. Touafek and E. M. Elsayed, “On the solutions of systems of rational difference equations,” Mathematical and Computer Modelling, vol. 55, no. 7-8, pp. 1987–1997, 2012. View at Publisher · View at Google Scholar · View at Scopus
  22. I. Yalçinkaya, “On the difference equation xn+1=α+xnm/xnk,” Discrete Dynamics in Nature and Society. An International Multidisciplinary Research and Review Journal, Article ID 805460, 8 pages, 2008.
  23. X. Yang, X. Liu, and L. Wang, “Stability of a generalized Putnam equation,” Applied Mathematics Letters, vol. 22, no. 4, pp. 565–568, 2009. View at Publisher · View at Google Scholar
  24. X. Yang, D. J. Evans, and G. M. Megson, “Global asymptotic stability in a class of Putnam-type equations,” Nonlinear Analysis A, vol. 64, no. 1, pp. 42–50, 2006. View at Publisher · View at Google Scholar
  25. X. Yang, “Global asymptotic stability in a class of generalized Putnam equations,” Journal of Mathematical Analysis and Applications, vol. 322, no. 2, pp. 693–698, 2006. View at Publisher · View at Google Scholar
  26. E. M. E. Zayed and M. A. El-Moneam, “On the rational recursive sequence xn+1=axn(bxn)/(cxn+dxnk),” Communications on Applied Nonlinear Analysis, vol. 15, no. 2, pp. 47–57, 2008.