Journal Menu

- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents

Abstract and Applied Analysis

Volume 2013 (2013), Article ID 179423, 10 pages

http://dx.doi.org/10.1155/2013/179423

Research Article

## On the Period-Two Cycles of

^{1}School of Mathematical Sciences, The National of University of Malaysia, 43600 Bangi, Selangor, Malaysia^{2}Department of Basic Sciences, King Saud bin Abdulaziz University for Health Sciences, Riyadh 11426, Saudi Arabia

Received 2 January 2013; Revised 13 April 2013; Accepted 13 April 2013

Academic Editor: Douglas Anderson

Copyright © 2013 S. Atawna 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

- M. Dehghan, M. J. Douraki, and M. Razzaghi, “Global stability of a higher order rational recursive sequence,”
*Applied Mathematics and Computation*, vol. 179, no. 1, pp. 161–174, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - M. Dehghan and R. Mazrooei-Sebdani, “The characteristics of a higher-order rational difference equation,”
*Applied Mathematics and Computation*, vol. 182, no. 1, pp. 521–528, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - M. Dehghan and R. Mazrooei-Sebdani, “Dynamics of a higher-order rational difference equation,”
*Applied Mathematics and Computation*, vol. 178, no. 2, pp. 345–354, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - M. Dehghan and N. Rastegar, “On the global behavior of a high-order rational difference equation,”
*Computer Physics Communications*, vol. 180, no. 6, pp. 873–878, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - E. M. E. Zayed, “Dynamics of the rational difference equation ${x}_{n+1}=(a{x}_{n}+b{x}_{n-k}+a{x}_{n}+b{x}_{n-k})/(c+d{x}_{n}{x}_{n-k})$,”
*Communications on Applied Nonlinear Analysis*, vol. 18, no. 4, pp. 39–56, 2011. View at MathSciNet - E. M. E. Zayed and M. A. El-Moneam, “On the rational recursive sequence ${x}_{n+1}=a{x}_{n}+(\beta {x}_{n}+\gamma {x}_{n-k})/(b{x}_{n}{x}_{n+k})$,”
*Communications on Applied Nonlinear Analysis*, vol. 16, no. 3, pp. 91–106, 2009. View at Zentralblatt MATH · View at MathSciNet - E. M. E. Zayed and M. A. El-Moneam, “On the rational recursive sequence ${x}_{n+1}=(a{x}_{n}+b{x}_{n-k}+\beta {x}_{n}+\gamma {x}_{n-k})/(C{x}_{n-k}+d{x}_{n-k})$,”
*Acta Applicandae Mathematicae*, vol. 111, no. 3, pp. 287–301, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - Y. S. and P. M. Knopf, “Boundedness of positive solutions of second-order rational difference equations,”
*Journal of Difference Equations and Applications*, vol. 10, no. 11, pp. 935–940, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - Y. S. Huang and P. M. Knopf, “Boundedness and some convergence properties of the difference equation ${x}_{n+1}=(\gamma {x}_{n-1}+\delta {x}_{n-2})/(B{x}_{n}+D{x}_{n2})$,”
*Journal of Difference Equations and Applications*, vol. 18, no. 1, pp. 27–55, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - R. Karatas, “Global behavior of a higher order difference equation,”
*Computers & Mathematics with Applications*, vol. 60, no. 3, pp. 830–839, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - R. Karatas and A. Gelişken, “Qualitative behavior of a rational difference equation,”
*Ars Combinatoria*, vol. 100, pp. 321–326, 2011. View at MathSciNet - 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. View at MathSciNet - S. N. Elaydi,
*An Introduction to Difference Equations*, Springer, New York, NY, USA, 2nd edition, 1999. View at MathSciNet - R. P. Agarwal,
*Difference Equations and Inequalities: Theory, Methods, and Applications*, vol. 228, Marcel Dekker, New York, NY, USA, 2nd edition, 2000. View at MathSciNet - M. R. S. Kulenović and G. Ladas,
*Dynamics of second-Order Rational Difference Equations with Open Problem and Conjectures*, Chapman & Hall/CRC, Boca Raton, Fla, USA, 2002. View at MathSciNet - E. Camouzis and G. Ladas,
*Dynamics of Third-Order Rational Difference Equations with Open Problem and Conjectures*, vol. 5, Chapman & Hall/CRC, Boca Raton, Fla, USA, 2008. View at MathSciNet - R. Abu-Saris, C. Çinar, and I. Yalçinkaya, “On the asymptotic stability of ${x}_{n+1}=(a+{x}_{n}{x}_{n-k})/({x}_{n}+{x}_{n-k})$,”
*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 - K. S. Berenhaut and S. Stević, “The global attractivity of a higher order rational difference equation,”
*Journal of Mathematical Analysis and Applications*, vol. 326, no. 2, pp. 940–944, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - Y.-H. Su and W.-T. Li, “Global attractivity of a higher order nonlinear difference equation,”
*Journal of Difference Equations and Applications*, vol. 11, no. 10, pp. 947–958, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - T. Sun and H. Xi, “Global asymptotic stability of a higher order rational difference equation,”
*Journal of Mathematical Analysis and Applications*, vol. 330, no. 1, pp. 462–466, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - Y. Wang, “On the dynamics of ${x}_{n+1}=(\beta {x}_{n}+\gamma {x}_{n-k})/(b{x}_{n}+C{x}_{n-k}+\alpha )$,”
*Journal of Difference Equations and Applications*, vol. 15, no. 10, pp. 949–961, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - H. Xi and T. Sun, “Global behavior of a higher-order rational difference equation,”
*Advances in Difference Equations*, Article ID 27637, 7 pages, 2006. View at Zentralblatt MATH · View at MathSciNet - X.-X. Yan, W.-T. Li, and Z. Zhao, “Global asymptotic stability for a higher order nonlinear rational difference equations,”
*Applied Mathematics and Computation*, vol. 182, no. 2, pp. 1819–1831, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - Y. Yang and F. B. Lv, “Dynamics of a higher order rational difference equation,”
*Advanced Materials Research*, vol. 216, pp. 50–55, 2011. View at Publisher · View at Google Scholar - S. Atawna, R. Abu-Saris, and I. Hashim, “Local stability of period two cycles of second order rational difference equation,”
*Discrete Dynamics in Nature and Society*, vol. 2012, Article ID 969813, 11 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - W. W. Hager,
*Applied Numerical Linear Algebra*, Prentice-Hall International Editions, 1988.