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Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 475038, 8 pages
http://dx.doi.org/10.1155/2012/475038
Research Article

The Dynamics of the Solutions of Some Difference Equations

1Department of Mathematics, College of Science and Arts, King Abdulaziz University, Rabigh Campus, P.O. Box 344, Rabigh 21911, Saudi Arabia
2Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
3Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Received 22 December 2011; Revised 17 May 2012; Accepted 17 May 2012

Academic Editor: Ibrahim Yalcinkaya

Copyright © 2012 H. El-Metwally 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. A. M. Amleh, E. A. Grove, G. Ladas, and D. A. Georgiou, “On the recursive sequence xn+1=α+xn-1/xn,” Journal of Mathematical Analysis and Applications, vol. 233, no. 2, pp. 790–798, 1999. View at Publisher · View at Google Scholar
  2. R. P. Agarwal, Difference Equations and Inequalities, vol. 228, Marcel Dekker, New York, NY, USA, 2nd edition, 2000.
  3. C. Çinar, “On the difference equation xn+1=xn-1/(-1+xnxn-1),” Applied Mathematics and Computation, vol. 158, no. 3, pp. 813–816, 2004. View at Publisher · View at Google Scholar
  4. C. Çinar, “On the positive solutions of the difference equation xn+1=axn-1/(1+bxnxn-1),” Applied Mathematics and Computation, vol. 156, no. 2, pp. 587–590, 2004. View at Publisher · View at Google Scholar
  5. E. M. Elabbasy, H. El-Metwally, and E. M. Elsayed, “On the difference equation xn+1=axn-(bxn)/(cxn-dxn-1),” Advances in Difference Equations, vol. 2006, Article ID 82579, 10 pages, 2006. View at Google Scholar
  6. E. M. Elabbasy, H. El-Metwally, and E. M. Elsayed, “On the difference equation xn+1=αxn-k/(β+γi=0kxn-i),” Journal of Concrete and Applicable Mathematics, vol. 5, no. 2, pp. 101–113, 2007. View at Google Scholar
  7. E. M. Elabbasy , H. El-Metwally, and E. M. Elsayed, “Global behavior of the solutions of difference equation,” Advances in Difference Equations, vol. 2011, 28 pages, 2011. View at Google Scholar
  8. H. El-Metwally, “Qualitative properties of some higher order difference equations,” Computers & Mathematics with Applications, vol. 58, no. 4, pp. 686–692, 2009. View at Publisher · View at Google Scholar
  9. H. M. El-Owaidy, A. M. Ahmed, and Z. Elsady, “Global attractivity of the recursive sequence xn+1=(α-βxn-k)/(γ+xn),” Journal of Applied Mathematics & Computing, vol. 16, no. 1-2, pp. 243–249, 2004. View at Publisher · View at Google Scholar
  10. 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
  11. 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
  12. E. A. Grove and G. Ladas, Periodicities in Nonlinear Difference Equations, vol. 4, Chapman & Hall/CRC, Boca Raton, Fla, USA, 2005.
  13. R. Karatas and C. Cinar, “On the solutions of the difference equation xn+1=(axn-(2k+2))/(-a+i=02k+2xn-i),” International Journal of Contemporary Mathematical Sciences, vol. 2, no. 13, pp. 1505–1509, 2007. View at Google Scholar
  14. V. L. Kocić and G. Ladas, Global Behavior of Nonlinear Difference Equations of Higher Order with Applications, vol. 256, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1993.
  15. 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.
  16. D. Simsek, C. Cinar, and I. Yalcinkaya, “On the recursive sequence xn+1=xn-3/(1+xn-1),” International Journal of Contemporary Mathematical Sciences, vol. 1, no. 10, pp. 475–480, 2006. View at Google Scholar
  17. S. Stević, “On the recursive sequence xn+1=xn-1/g(xn),” Taiwanese Journal of Mathematics, vol. 6, no. 3, pp. 405–414, 2002. View at Google Scholar
  18. C. Wang and S. Wang, “Oscillation of partial population model with diffusion and delay,” Applied Mathematics Letters, vol. 22, no. 12, pp. 1793–1797, 2009. View at Publisher · View at Google Scholar
  19. I. Yalcinkaya, “On the global attractivity of positive solutions of a rational difference equation,” Selçuk Journal of Applied Mathematics, vol. 9, no. 2, pp. 3–8, 2008. View at Google Scholar
  20. I. Yalçinkaya, C. Çinar, and M. Atalay, “On the solutions of systems of difference equations,” Advances in Difference Equations, vol. 2008, Article ID 143943, 9 pages, 2008. View at Google Scholar
  21. I. Yalçinkaya, C. Çinar, and M. Atalay, “On the solutions of systems of difference equations,” Advances in Difference Equations, vol. 2008, Article ID 143943, 9 pages, 2008. View at Google Scholar
  22. I. Yalcinkaya, “On the global asymptotic stability of a second-order system of difference equations,” Discrete Dynamics in Nature and Society, vol. 2008, Article ID 860152, 12 pages, 2008. View at Publisher · View at Google Scholar
  23. I. Yalçinkaya, “On the difference equation xn+1=α+(xn-m/xnk),” Discrete Dynamics in Nature and Society, vol. 2008, Article ID 805460, 8 pages, 2008. View at Google Scholar