Discrete Dynamics in Nature and Society

Volume 2012, Article ID 105496, 9 pages

http://dx.doi.org/10.1155/2012/105496

Research Article

## On the Behavior of a System of Rational Difference Equations =

^{1}School of Mathematics, North China University of Water Resources and Electric Power, Zhengzhou 450045, China^{2}School of Economics and Finance, Xi'an Jiaotong University, Xi'an 710061, China

Received 28 June 2012; Accepted 24 August 2012

Academic Editor: Cengiz Çinar

Copyright © 2012 Liu Keying 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

- Y. Gu and R. Ding, “Observable state space realizations for multivariable systems,”
*Computers and Mathematics with Applications*, vol. 63, no. 9, pp. 1389–1399, 2012. View at Google Scholar - M. R. S. Kulenović and G. Ladas,
*Dynamics of Second Order Rational Difference Equations*, Chapman & Hall/CRC, Boca Raton, Fla, USA, 2002. View at Zentralblatt MATH - K. Liu, P. Cheng, P. Li, and W. Zhong, “On a system of rational difference equations ${x}_{n+1}={x}_{n-1}/({y}_{n}{x}_{n-1}-1),{y}_{n+1}={y}_{n-1}/({x}_{n}{y}_{n-1}-1),{z}_{n+1}=1/{y}_{n}{z}_{n-1}$,”
*Fasciculi Mathematici*. In press. - C. Çinar, “On the positive solutions of the difference equation ${x}_{n+1}={x}_{n-1}/(1+b{x}_{n}{x}_{n-1})$,”
*Applied Mathematics and Computation*, vol. 150, no. 1, pp. 21–24, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - C. Çinar, “On the positive solutions of the difference equation ${x}_{n+1}=a{x}_{n-1}/(1+b{x}_{n}{x}_{n-1})$,”
*Applied Mathematics and Computation*, vol. 156, no. 2, pp. 587–590, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - 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 Publisher · View at Google Scholar · View at Zentralblatt MATH - S. Stević, “On a system of difference equations ${x}_{n+1}=a{x}_{n-1}/(b{y}_{n}{x}_{n-1}+c),{y}_{n+1}=\alpha {y}_{n-1}/(\beta {x}_{n}{y}_{n-1}+\gamma )$,”
*Applied Mathematics and Computation*, vol. 218, no. 7, pp. 3372–3378, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - A. S. Kurbanli, C. Çinar, and I. Yalçinkaya, “On the behavior of solutions of the system of rational difference equations ${x}_{n+1}={x}_{n-1}/({y}_{n}{x}_{n-1}-1),{y}_{n+1}={y}_{n-1}/({x}_{n}{y}_{n-1}-1)$,”
*World Applied Sciences Journal*, vol. 10, no. 11, pp. 1344–1350, 2010. View at Google Scholar - A. S. Kurbanli, “On the behavior of solutions of the system of rational difference equations ${x}_{n+1}={x}_{n-1}/({y}_{n}{x}_{n-1}-1),{y}_{n+1}={y}_{n-1}/({x}_{n}{y}_{n-1}-1),{z}_{n+1}={z}_{n-1}/({y}_{n}{z}_{n-1}-1)$,”
*Discrete Dynamics in Nature and Society*, vol. 2011, Article ID 932632, 12 pages, 2011. View at Publisher · View at Google Scholar - A. S. Kurbanli, “On the behavior of solutions of the system of rational difference equations ${x}_{n+1}={x}_{n-1}/({y}_{n}{x}_{n-1}-1),{y}_{n+1}={y}_{n-1}/({x}_{n}{y}_{n-1}-1),{z}_{n+1}=1/{y}_{n}{z}_{n}$,”
*Advances in Difference Equations*, vol. 40, 2011. View at Google Scholar - A. S. Kurbanli, C. Çinar, and M. E. Erdoğan, “On the behavior of solutions of the system of rational difference equations of rational difference equations ${x}_{n+1}={x}_{n-1}/({y}_{n}{x}_{n-1}-1),{y}_{n+1}={y}_{n-1}/({x}_{n}{y}_{n-1}-1),{z}_{n+1}={x}_{n}/{y}_{n}{z}_{n-1}$,”
*Applied Methematics*, vol. 2, pp. 1031–1038, 2011. View at Google Scholar - 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