Table of Contents Author Guidelines Submit a Manuscript
Discrete Dynamics in Nature and Society
Volume 2016, Article ID 6842521, 7 pages
http://dx.doi.org/10.1155/2016/6842521
Research Article

Global Character of a Six-Dimensional Nonlinear System of Difference Equations

Department of Mathematics, Faculty of Science and Arts, Bülent Ecevit University, 67100 Zonguldak, Turkey

Received 25 November 2015; Accepted 2 June 2016

Academic Editor: Zhan Zhou

Copyright © 2016 Mehmet Gümüş and Yüksel Soykan. 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. Q. Din and E. M. Elsayed, “Stability analysis of a discrete ecological model,” Computational Ecology and Software, vol. 4, no. 2, pp. 89–103, 2014. View at Google Scholar
  2. A. Q. Khan, Q. Din, M. N. Qureshi, and T. F. Ibrahim, “Global behavior of an anti-competitive system of fourth-order rational difference equations,” Computational Ecology and Software, vol. 4, no. 1, pp. 35–46, 2014. View at Google Scholar
  3. E. M. Elsayed, “Solutions of rational difference systems of order two,” Mathematical and Computer Modelling, vol. 55, no. 3-4, pp. 378–384, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  4. A. Q. Khan, M. N. Qureshi, and Q. Din, “Global dynamics of some systems of higher-order rational difference equations,” Advances in Difference Equations, vol. 2013, article 354, 2013. View at Publisher · View at Google Scholar · View at Scopus
  5. A. Y. Özban, “On the system of rational difference equations xn=a/yn-3,yn=byn-3/xn-qyn-q,” Applied Mathematics and Computation, vol. 188, no. 1, pp. 833–837, 2007. View at Publisher · View at Google Scholar · View at Scopus
  6. I. Yalcinkaya, “On 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 Publisher · View at Google Scholar · View at Scopus
  7. I. Yalcinkaya, C. Cinar, and D. Simsek, “Global asymptotic stability of a system of difference equations,” Applicable Analysis, vol. 87, no. 6, pp. 677–687, 2008. View at Publisher · View at Google Scholar
  8. R. Abo-Zeid, “Global attractivity of a higher-order difference equation,” Discrete Dynamics in Nature and Society, vol. 2012, Article ID 930410, 11 pages, 2012. View at Publisher · View at Google Scholar · View at Scopus
  9. D. Chen, X. Li, and Y. Wang, “Dynamics for nonlinear difference equation xn+1=(αxn-k)/(β+γxn-1p),” Advances in Difference Equations, vol. 2009, Article ID 235691, 2009. View at Publisher · View at Google Scholar · View at Scopus
  10. H. M. El-Owaidy, A. M. Youssef, and A. M. Ahmed, “On the Dynamics of xn+1=bxn-12A+Bxn-2-1,” Rostocker Mathematisches Kolloquium, vol. 59, pp. 11–18, 2005. View at Google Scholar
  11. M. Gümüş, “The periodicity of positive solutions of the non-linear difference equation xn+1=α+(xnkp)/(xnq),” Discrete Dynamics in Nature and Society, vol. 2013, Article ID 742912, 3 pages, 2013. View at Publisher · View at Google Scholar
  12. Ö. Öcalan, H. Ogünmez, and M. Gümüş, “Global behavior test for a nonlinear difference equation with a period-two coefficient,” Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis, vol. 21, no. 3-4, pp. 307–316, 2014. View at Google Scholar · View at Scopus
  13. A. S. Kurbanlı, C. Çinar, and I. Yalçinkaya, “On the behavior of positive solutions of the system of rational difference equations xn+1=xn-1/ynxn-1+1, yn+1=yn-1/xnyn-1+1,” Mathematical and Computer Modelling, vol. 53, no. 5, pp. 1261–1267, 2011. View at Publisher · View at Google Scholar
  14. G. Papaschinopoulos and C. J. Schinas, “On a system of two nonlinear difference equations,” Journal of Mathematical Analysis and Applications, vol. 219, no. 2, pp. 415–426, 1998. View at Publisher · View at Google Scholar · View at Scopus
  15. Q. Zhang, L. Yang, and J. Liu, “Dynamics of a system of rational third-order difference equation,” Advances in Difference Equations, vol. 2012, article 136, 2012. View at Publisher · View at Google Scholar · View at Scopus
  16. Q. Din, M. N. Qureshi, and A. Q. Khan, “Dynamics of a fourth-order system of rational difference equations,” Advances in Difference Equations, vol. 2012, no. 1, article 215, 15 pages, 2012. View at Google Scholar
  17. 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 Zentralblatt MATH · View at Scopus
  18. H. M. El-Owaidy, A. M. Ahmed, and A. M. Youssef, “The dynamics of the recursive sequence xn+1=(αxn-1)/(β+γxn-2p),” Applied Mathematics Letters, vol. 18, no. 9, pp. 1013–1018, 2005. View at Publisher · View at Google Scholar · View at Scopus
  19. E. Camouzis and G. Ladas, Dynamics of Third-Order Rational Difference Equations with Open Problems and Conjectures, vol. 5, CRC Press, 2007.
  20. V. L. Kocic and G. Ladas, Global Behavior of Nonlinear Difference Equations of Higher Order with Applications, Kluwer Academic, Dordrecht, The Netherlands, 1993.
  21. M. R. S. Kulenović and G. Ladas, Dynamics of Second Order Rational Difference Equations, Chapman & Hall/CRC Press, 2001.
  22. H. Sedaghat, Nonlinear Difference Equations Theory with Applications to Social Science Models, vol. 15, Springer, 2003.