Journal of Difference Equations

Volume 2015 (2015), Article ID 396757, 7 pages

http://dx.doi.org/10.1155/2015/396757

Research Article

## Some General Systems of Rational Difference Equations

Mathematics Department, Kamil Özdağ Faculty of Science, Karamanoğlu Mehmetbey University, 70100 Karaman, Turkey

Received 17 December 2014; Accepted 18 February 2015

Academic Editor: Mustafa R. S. Kulenović

Copyright © 2015 Ali Gelisken and Merve Kara. 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

- C. Çinar, “On the positive solutions of the difference equation system ${x}_{n+1}=1/{y}_{n},{y}_{n+1}={y}_{n}/{x}_{n-1}{y}_{n-1}$,”
*Applied Mathematics and Computation*, vol. 158, no. 2, pp. 303–305, 2004. View at Google Scholar - A. S. Kurbanli, C. Çinar, and I. Yalçinkaya, “On the behavior of positive solutions of the system of rational difference equations ${x}_{n+1}={x}_{n-1}/({y}_{n}{x}_{n-1}+1),{y}_{n+1}={y}_{n-1}/({x}_{n}{y}_{n-1}+1)$,”
*Mathematical and Computer Modelling*, vol. 53, no. 5-6, pp. 1261–1267, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus - E. M. Elsayed, “On the solutions of a rational system of difference equations,”
*Fasciculi Mathematici*, no. 45, pp. 26–36, 2010. View at Google Scholar - E. M. Elsayed, “Solutions of rational difference systems of order two ${x}_{n+1}={x}_{n-1}/\pm 1+{x}_{n-1}{y}_{n}$, ${y}_{n+1}={y}_{n-1}/\pm 1+{y}_{n-1}{x}_{n}$,”
*Mathematical and Computer Modelling*, vol. 55, no. 3-4, pp. 378–384, 2012. View at Google Scholar - 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 MathSciNet · View at Scopus - 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 MathSciNet - O. Özkan and A. S. Kurbanli, “On a system of difference equations,”
*Discrete Dynamics in Nature and Society*, vol. 2013, Article ID 970316, 7 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet - E. M. Elabbasy, H. El-Metwally, and E. M. Elsayed, “On the solutions of a class of difference equations systems,”
*Demonstratio Mathematica*, vol. 41, no. 1, pp. 109–122, 2008. View at Google Scholar · View at MathSciNet - E. M. Elsayed, “On the solutions of higher order rational system of recursive sequences,”
*Mathematica Balkanica. New Series*, vol. 22, no. 3-4, pp. 287–296, 2008. View at Google Scholar · View at MathSciNet - E. M. Elsayed, M. M. El-Dessoky, and A. Alotaibi, “On the solutions of a general system of difference equations,”
*Discrete Dynamics in Nature and Society*, vol. 2012, Article ID 892571, 12 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus - A. S. Kurbanli, C. Çinar, and D. Şimşek, “On the periodicity of solutions of the system of rational difference equations ${x}_{n+1}=({x}_{n-1}+{y}_{n})/({y}_{n}{x}_{n-1}-1)$, ${y}_{n+1}=({y}_{n-1}+{x}_{n})/({x}_{n}{y}_{n-1}-1)$,”
*Applied Mathematics*, vol. 2, no. 4, pp. 410–413, 2011. View at Publisher · View at Google Scholar · View at MathSciNet - A. Y. Özban, “On the system of rational difference equations ${x}_{n}=a/{y}_{n-3},{y}_{n}=b{y}_{n-3}/{x}_{n-q}{y}_{n-q}$,”
*Applied Mathematics and Computation*, vol. 188, no. 1, pp. 833–837, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus - A. Y. Özban, “On the positive solutions of the system of rational difference equations ${x}_{n+1}=1/{y}_{n-k}\mathrm{}$, ${y}_{n+1}={x}_{n}/({x}_{n-m}\mathrm{}{y}_{n-m-k})$,”
*Journal of Mathematical Analysis and Applications*, vol. 323, no. 1, pp. 26–32, 2006. View at Google Scholar - 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 Google Scholar · View at MathSciNet · View at Scopus - 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 MathSciNet · View at Scopus