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Discrete Dynamics in Nature and Society
Volume 2011 (2011), Article ID 932362, 12 pages
http://dx.doi.org/10.1155/2011/932362
Research Article

On the Behavior of Solutions of the System of Rational Difference Equations: π‘₯ 𝑛 + 1 = π‘₯ 𝑛 βˆ’ 1 / ( 𝑦 𝑛 π‘₯ 𝑛 βˆ’ 1 βˆ’ 1 ) , 𝑦 𝑛 + 1 = 𝑦 𝑛 βˆ’ 1 / ( π‘₯ 𝑛 𝑦 𝑛 βˆ’ 1 βˆ’ 1 ) , and 𝑧 𝑛 + 1 = 𝑧 𝑛 βˆ’ 1 / ( 𝑦 𝑛 𝑧 𝑛 βˆ’ 1 βˆ’ 1 )

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

Received 23 December 2010; Accepted 26 January 2011

Academic Editor: Ibrahim Yalcinkaya

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.

Linked References

  1. C. Çinar, β€œOn the positive solutions of the difference equation system xn+1=1/yn, yn+1=yn/xn1yn1,” Applied Mathematics and Computation, vol. 158, no. 2, pp. 303–305, 2004. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  2. G. Papaschinopoulos and C. J. Schinas, β€œOn a system of two nonlinear difference equations,” Journal of Mathematical Analysis and Applications, vol. 219, no. 2, pp. 415–426, 1998. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  3. G. Papaschinopoulos and C. J. Schinas, β€œOn the system of two difference equations,” Journal of Mathematical Analysis and Applications, vol. 273, no. 2, pp. 294–309, 2002. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  4. A. Y. Özban, β€œOn the system of rational difference equations xn=a/yn3, yn=byn3/xnqynq,” Applied Mathematics and Computation, vol. 188, no. 1, pp. 833–837, 2007. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  5. A. Y. Özban, β€œOn the positive solutions of the system of rational difference equations xn+1=1/ynk, yn+1=yn/xnmynmk,” Journal of Mathematical Analysis and Applications, vol. 323, no. 1, pp. 26–32, 2006. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  6. D. Clark and M. R. S. Kulenović, β€œA coupled system of rational difference equations,” Computers & Mathematics with Applications, vol. 43, no. 6-7, pp. 849–867, 2002. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  7. D. Clark, M. R. S. Kulenović, and J. F. Selgrade, β€œGlobal asymptotic behavior of a two-dimensional difference equation modelling competition,” Nonlinear Analysis. Theory, Methods & Applications, vol. 52, no. 7, pp. 1765–1776, 2003. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  8. E. Camouzis and G. Papaschinopoulos, β€œGlobal asymptotic behavior of positive solutions on the system of rational difference equations xn+1=1+xn/ynm , yn+1=1+yn/xnm,” Applied Mathematics Letters, vol. 17, no. 6, pp. 733–737, 2004. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  9. X. Yang, Y. Liu, and S. Bai, β€œOn the system of high order rational difference equations xn=a/ynp,yn=bynp/xnqynq,” Applied Mathematics and Computation, vol. 171, no. 2, pp. 853–856, 2005. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  10. M. R. S. Kulenović and Z. Nurkanović, β€œGlobal behavior of a three-dimensional linear fractional system of difference equations,” Journal of Mathematical Analysis and Applications, vol. 310, no. 2, pp. 673–689, 2005. View at Google Scholar Β· View at Zentralblatt MATH
  11. Y. Zhang, X. Yang, G. M. Megson, and D. J. Evans, β€œOn the system of rational difference equations xn=A+1/ynp, yn=A+yn1/xnryns,” Applied Mathematics and Computation, vol. 176, no. 2, pp. 403–408, 2006. View at Publisher Β· View at Google Scholar Β· View at MathSciNet
  12. Y. Zhang, X. Yang, D. J. Evans, and C. Zhu, β€œOn the nonlinear difference equation system xn+1=A+ynm/xn, yn+1=A+xnm/yn,” Computers & Mathematics with Applications, vol. 53, no. 10, pp. 1561–1566, 2007. View at Publisher Β· View at Google Scholar Β· View at MathSciNet
  13. I. Yalcinkaya, β€œOn the global asymptotic behavior of a system of two nonlinear difference equations,” Ars Combinatoria, vol. 95, pp. 151–159, 2010. View at Google Scholar
  14. I. Yalcinkaya, C. Çinar, and M. Atalay, β€œOn the solutions of systems of difference equations,” Advances in Difference Equations, vol. 2008, Article ID 143943, 9 pages, 2008. View at Google Scholar Β· View at Zentralblatt MATH
  15. I. Yalcinkaya, β€œOn 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 Google Scholar Β· View at Zentralblatt MATH
  16. B. D. Irićanin and S. Stević, β€œSome systems of nonlinear difference equations of higher order with periodic solutions,” Dynamics of Continuous, Discrete & Impulsive Systems. Series A. Mathematical Analysis, vol. 13, no. 3-4, pp. 499–507, 2006. View at Google Scholar Β· View at Zentralblatt MATH
  17. A. S. Kurbanlı, C. Çinar, and I. Yalcinkaya, β€œOn the behavaior of positive solutions of the system of rational difference equations xn+1=xn1/(ynxn1)+1, yn+1=yn1/(xnyn1)+1,” Mathematical and Computer Modelling, vol. 53, no. 5-6, pp. 1261–1267, 2011. View at Google Scholar