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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 495838, 6 pages
http://dx.doi.org/10.1155/2013/495838
Research Article

Qualitative Behavior of Rational Difference Equation of Big Order

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

Received 4 February 2013; Accepted 20 April 2013

Academic Editor: Cengiz Çinar

Copyright © 2013 M. M. El-Dessoky. 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. Abu-Saris, C. Çinar, and I. Yalçinkaya, “On the asymptotic stability of xn+1=a+xnxn-k/xn+xn-k,” Computers & Mathematics with Applications, vol. 56, no. 5, pp. 1172–1175, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. R. P. Agarwal, Difference Equations and Inequalities, Marcel Dekker, New York, NY, USA, 1st edition, 1992. View at MathSciNet
  3. R. P. Agarwal, Difference Equations and Inequalities, Marcel Dekker, New York, NY, USA, 2nd edition, 2000. View at MathSciNet
  4. R. P. Agarwal and E. M. Elsayed, “Periodicity and stability of solutions of higher order rational difference equation,” Advanced Studies in Contemporary Mathematics, vol. 17, no. 2, pp. 181–201, 2008. View at Zentralblatt MATH · View at MathSciNet
  5. M. Aloqeili, “Dynamics of a rational difference equation,” Applied Mathematics and Computation, vol. 176, no. 2, pp. 768–774, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. N. Battaloglu, C. Cinar, and I. Yalçınkaya, “The dynamics of the difference equation,” Ars Combinatoria, vol. 97, pp. 281–288, 2010. View at Zentralblatt MATH · View at MathSciNet
  7. 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 · View at Zentralblatt MATH · View at MathSciNet
  8. 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 Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. E. M. Elabbasy, H. El-Metwally, and E. M. Elsayed, “On the difference equation xn+1=axn-k/β+γi=0kxn-i,” Journal of Concrete and Applicable Mathematics, vol. 5, no. 2, pp. 101–113, 2007. View at Zentralblatt MATH · View at MathSciNet
  10. E. M. Elabbasy, H. El-Metwally, and E. M. Elsayed, “Qualitative behavior of higher order difference equation,” Soochow Journal of Mathematics, vol. 33, no. 4, pp. 861–873, 2007. View at Zentralblatt MATH · View at MathSciNet
  11. S. Kang and B. Shi, “Periodic solutions for a system of difference equations,” Discrete Dynamics in Nature and Society, vol. 2009, Article ID 760328, 9 pages, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. A. Y. Őzban, “On the system of rational difference equations xn=a/yn-3, yn=byn-3/xn-qyn-q,” Applied Mathematics and Computation, vol. 188, no. 1, pp. 833–837, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. E. Camouzis and G. Papaschinopoulos, “Global asymptotic behavior of positive solutions on the system of rational difference equations xn+1=1+xn/yn-m, yn+1=1+yn/xn-m,” Applied Mathematics Letters, vol. 17, no. 6, pp. 733–737, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. E. M. Elabbasy and E. M. Elsayed, “Global asymptotic behavior attractivity and periodic nature of a difference equation,” World Applied Sciences Journal, vol. 12, no. 1, pp. 39–47, 2011.
  15. V. L. Kocić and G. Ladas, Global Behavior of Nonlinear Difference Equations of Higher Order with Applications, Kluwer Academic, Dordrecht, The Netherlands, 1993. View at MathSciNet
  16. 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, 2001. View at MathSciNet
  17. I. Yalçinkaya, “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 · View at Zentralblatt MATH · View at MathSciNet
  18. H. El-Metwally, “Global behavior of an economic model,” Chaos, Solitons & Fractals, vol. 33, no. 3, pp. 994–1005, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. I. Yalçinkaya, “On the global asymptotic behavior of a system of two nonlinear difference equations,” Ars Combinatoria, vol. 95, pp. 151–159, 2010. View at Zentralblatt MATH · View at MathSciNet
  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 Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. J. Diblík, B. Iricanin, S. Stevic, and Z. Šmarda, “On some symmetric systems of difference equations,” Abstract and Applied Analysis, vol. 2013, Article ID 246723, 7 pages, 2013. View at Publisher · View at Google Scholar
  22. E. M. Elsayed, “Dynamics of a recursive sequence of higher order,” Communications on Applied Nonlinear Analysis, vol. 16, no. 2, pp. 37–50, 2009. View at Zentralblatt MATH · View at MathSciNet
  23. M. Saleh and M. Aloqeili, “On the difference equation yn+1=A+yn/yn-k with A<0,” Applied Mathematics and Computation, vol. 176, no. 1, pp. 359–363, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. C. Wang, S. Wang, Z. Wang, H. Gong, and R. Wang, “Asymptotic stability for a class of nonlinear difference equation,” Discrete Dynamics in Natural and Society, vol. 2010, Article ID 791610, 10 pages, 2010. View at Publisher · View at Google Scholar
  25. C.-y. Wang, Q.-h. Shi, and S. Wang, “Asymptotic behavior of equilibrium point for a family of rational difference equations,” Advances in Difference Equations, vol. 2010, Article ID 505906, 10 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  26. 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 Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  27. E. M. E. Zayed and M. A. El-Moneam, “On the rational recursive sequence ,” Communications on Applied Nonlinear Analysis, vol. 15, no. 2, pp. 47–57, 2008. View at Zentralblatt MATH · View at MathSciNet
  28. E. M. E. Zayed and M. A. EL-Moneam, “On the rational recursive sequence xn+1=α+βxn+γxn-1/A+Bxn+Cxn-1,” Communications on Applied Nonlinear Analysis, vol. 12, no. 4, pp. 15–28, 2005. View at Zentralblatt MATH · View at MathSciNet
  29. E. M. Elsayed and M. M. El-Dessoky, “Dynamics and behavior of a higher order rational recursive sequence,” Advances in Difference Equations, pp. 2012–69, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  30. D. Simsek, B. Demir, and C. Cinar, “On the solutions of the system of difference equations xn+1=max{A/xn,yn/xn}, yn+1=max{A/yn,xn/yn},” Discrete Dynamics in Nature and Society, vol. 2011, Article ID 325296, 11 pages, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  31. M. Mansour, M. M. El-Dessoky, and E. M. Elsayed, “The form of the solutions and periodicity of some systems of difference equations,” Discrete Dynamics in Nature and Society, vol. 2012, Article ID 406821, 17 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  32. B. D. Iričanin and S. Stević, “Some systems of nonlinear difference equations of higher order with periodic solutions,” Dynamics of Continuous, Discrete & Impulsive Systems A, vol. 13, no. 3-4, pp. 499–507, 2006. View at Zentralblatt MATH · View at MathSciNet
  33. A. Gelisken, C. Cinar, and I. Yalcinkaya, “On a max-type difference equation,” Advances in Difference Equations, vol. 2010, Article ID 584890, 6 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  34. C. Wang, S. Wang, L. Li, and Q. Shi, “Asymptotic behavior of equilibrium point for a class of nonlinear difference equation,” Advances in Difference Equations, vol. 2009, Article ID 214309, 8 pages, 2009. View at Publisher · View at Google Scholar
  35. C.-Y. Wang, S. Wang, Z.-w. Wang, F. Gong, and R.-f. Wang, “Asymptotic stability for a class of nonlinear difference equations,” Discrete Dynamics in Nature and Society. An International Multidisciplinary Research and Review Journal, vol. 2010, Article ID 791610, 10 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  36. X. Zhang, L. Liu, Y. Wu, and Y. Lu, “The iterative solutions of nonlinear fractional differential equations,” Applied Mathematics and Computation, vol. 219, no. 9, pp. 4680–4691, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  37. A. S. Kurbanli, “On the behavior of solutions of the system of rational difference equations: xn+1=xn-1/ynxn-1-1, xn+1=yn-1/xnyn-1-1 and zn+1=zn-1/ynzn-1-1,” Discrete Dynamics in Nature and Society. An International Multidisciplinary Research and Review Journal, vol. 2011, Article ID 932362, 12 pages, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  38. K. Liu, Z. Zhao, X. Li, and P. Li, “More on three-dimensional systems of rational difference equations,” Discrete Dynamics in Nature and Society, vol. 2011, Article ID 178483, 9 pages, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  39. S. Stević, “On a system of difference equations,” Applied Mathematics and Computation, vol. 218, no. 7, pp. 3372–3378, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet