`Discrete Dynamics in Nature and SocietyVolume 2011, Article ID 932362, 12 pageshttp://dx.doi.org/10.1155/2011/932362`
Research Article

## On the Behavior of Solutions of the System of Rational Difference Equations: π₯ π + 1 = π₯ π β 1 / ( π¦ π π₯ π β 1 β 1 ) , π¦ π + 1 = π¦ π β 1 / ( π₯ π π¦ π β 1 β 1 ) , and π§ π + 1 = π§ π β 1 / ( π¦ π π§ π β 1 β 1 )

Department of Mathematics, Faculty of Education, Selcuk University, 42090 Konya, Turkey

Received 23 December 2010; Accepted 26 January 2011

Copyright © 2011 Abdullah Selçuk Kurbanli. 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.

1. C. Çinar, βOn the positive solutions of the difference equation system ${x}_{n+1}=1/{y}_{n}$, ${y}_{n+1}={y}_{n}/{x}_{n-1}{y}_{n-1}$,β Applied Mathematics and Computation, vol. 158, no. 2, pp. 303β305, 2004.
2. G. Papaschinopoulos and C. J. Schinas, βOn a system of two nonlinear difference equations,β Journal of Mathematical Analysis and Applications, vol. 219, no. 2, pp. 415β426, 1998.
3. G. Papaschinopoulos and C. J. Schinas, βOn the system of two difference equations,β Journal of Mathematical Analysis and Applications, vol. 273, no. 2, pp. 294β309, 2002.
4. A. Y. Özban, βOn the system of rational difference equations ${x}_{n}=a/{y}_{n-3}$, ${y}_{n}=b{y}_{n-3}/{x}_{n-q}{y}_{n-q}$,β Applied Mathematics and Computation, vol. 188, no. 1, pp. 833β837, 2007.
5. A. Y. Özban, βOn the positive solutions of the system of rational difference equations ${x}_{n+1}=1/{y}_{n-k}$, ${y}_{n+1}={y}_{n}/{x}_{n-m}{y}_{n-m-k}$,β Journal of Mathematical Analysis and Applications, vol. 323, no. 1, pp. 26β32, 2006.
6. D. Clark and M. R. S. Kulenović, βA coupled system of rational difference equations,β Computers & Mathematics with Applications, vol. 43, no. 6-7, pp. 849β867, 2002.
7. D. Clark, M. R. S. Kulenović, and J. F. Selgrade, βGlobal asymptotic behavior of a two-dimensional difference equation modelling competition,β Nonlinear Analysis. Theory, Methods & Applications, vol. 52, no. 7, pp. 1765β1776, 2003.
8. E. Camouzis and G. Papaschinopoulos, βGlobal asymptotic behavior of positive solutions on the system of rational difference equations ${x}_{n+1}=1+{x}_{n}/{y}_{n-m}$ , ${y}_{n+1}=1+{y}_{n}/{x}_{n-m}$,β Applied Mathematics Letters, vol. 17, no. 6, pp. 733β737, 2004.
9. X. Yang, Y. Liu, and S. Bai, βOn the system of high order rational difference equations ${x}_{n}=a/{y}_{n-p},{y}_{n}=b{y}_{n-p}/{x}_{n-q}{y}_{n-q}$,β Applied Mathematics and Computation, vol. 171, no. 2, pp. 853β856, 2005.
10. M. R. S. Kulenović and Z. Nurkanović, βGlobal behavior of a three-dimensional linear fractional system of difference equations,β Journal of Mathematical Analysis and Applications, vol. 310, no. 2, pp. 673β689, 2005.
11. Y. Zhang, X. Yang, G. M. Megson, and D. J. Evans, βOn the system of rational difference equations ${x}_{n}=A+1/{y}_{n-p}$, ${y}_{n}=A+{y}_{n-1}/{x}_{n-r}{y}_{n-s}$,β Applied Mathematics and Computation, vol. 176, no. 2, pp. 403β408, 2006.
12. Y. Zhang, X. Yang, D. J. Evans, and C. Zhu, βOn the nonlinear difference equation system ${x}_{n+1}=A+{y}_{n-m}/{x}_{n}$, ${y}_{n+1}=A+{x}_{n-m}/{y}_{n}$,β Computers & Mathematics with Applications, vol. 53, no. 10, pp. 1561β1566, 2007.
13. I. Yalcinkaya, βOn the global asymptotic behavior of a system of two nonlinear difference equations,β Ars Combinatoria, vol. 95, pp. 151β159, 2010.
14. I. Yalcinkaya, C. Çinar, and M. Atalay, βOn the solutions of systems of difference equations,β Advances in Difference Equations, vol. 2008, Article ID 143943, 9 pages, 2008.
15. I. Yalcinkaya, βOn the global asymptotic stability of a second-order system of difference equations,β Discrete Dynamics in Nature and Society, vol. 2008, Article ID 860152, 12 pages, 2008.
16. B. D. Irićanin and S. Stević, βSome systems of nonlinear difference equations of higher order with periodic solutions,β Dynamics of Continuous, Discrete & Impulsive Systems. Series A. Mathematical Analysis, vol. 13, no. 3-4, pp. 499β507, 2006.
17. A. S. Kurbanlı, C. Çinar, and I. Yalcinkaya, βOn the behavaior of positive solutions of the system of rational difference equations ${x}_{n+1}={x}_{n-1}/\left({y}_{n}{x}_{n-1}\right)+1$, ${y}_{n+1}={y}_{n-1}/\left({x}_{n}{y}_{n-1}\right)+1$,β Mathematical and Computer Modelling, vol. 53, no. 5-6, pp. 1261β1267, 2011.