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Abstract and Applied Analysis

Volume 2014 (2014), Article ID 982378, 6 pages

http://dx.doi.org/10.1155/2014/982378

## On the Periodicity of Some Classes of Systems of Nonlinear Difference Equations

^{1}Mathematical Institute of the Serbian Academy of Sciences, Knez Mihailova 36/III, 11000 Beograd, Serbia^{2}Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia^{3}Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 42641, Jeddah 21551, Saudi Arabia

Received 25 September 2013; Revised 3 December 2013; Accepted 4 December 2013; Published 23 January 2014

Academic Editor: Josef Diblik

Copyright © 2014 Stevo Stević 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

- G. Bastien and M. Rogalski, “Global behaviour of solutions of cyclic systems of $q$ order 2 or 3 generalized Lyness' difference equations and of other more general equations of higher order,”
*Journal of Difference Equations and Applications*, vol. 17, no. 11, pp. 1651–1672, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - E. M. Elsayed, B. Iričanin, and S. Stević, “On the max-type equation ${x}_{n+1}=\text{max}\{{A}_{n}/{x}_{n},{x}_{n-1}\}$,”
*Ars Combinatoria*, vol. 95, pp. 187–192, 2010. View at Zentralblatt MATH · View at MathSciNet - E. A. Grove and G. Ladas,
*Periodicities in Nonlinear Difference Equations*, vol. 4 of*Advances in Discrete Mathematics and Applications*, Chapman & Hall, CRC Press, Boca Raton, Fla, USA, 2005. View at MathSciNet - B. D. Iričanin and S. Stević, “Some systems of nonlinear difference equations of higher order with periodic solutions,”
*Dynamics of Continuous, Discrete & Impulsive Systems A*, vol. 13, no. 3-4, pp. 499–507, 2006. View at Zentralblatt MATH · View at MathSciNet - B. D. Iričanin and N. Touafek, “On a second-order max-type system of difference equations,”
*Indian Journal of Mathematics*, vol. 54, no. 1, pp. 119–142, 2012. View at Zentralblatt MATH · View at MathSciNet - C. M. Kent, M. Kustesky, A. Q. Nguyen, and B. V. Nguyen, “Eventually periodic solutions of ${x}_{n+1}=\text{max}\{{A}_{n}/{x}_{n},{B}_{n}/{x}_{n-1}\}$ when the parameters are two cycles,”
*Dynamics of Continuous, Discrete & Impulsive Systems A*, vol. 10, no. 1–3, pp. 33–49, 2003. View at Zentralblatt MATH · View at MathSciNet - C. M. Kent and M. A. Radin, “On the boundedness nature of positive solutions of the difference equation ${x}_{n+1}=\text{max}\{{A}_{n}/{x}_{n},{B}_{n}/{x}_{n-1}\}$ with periodic parameters,”
*Dynamics of Continuous, Discrete & Impulsive Systems B*, supplement, pp. 11–15, 2003. View at MathSciNet - W. Kosmala, “A period 5 difference equation,”
*International Journal of Nonlinear Analysis and Applications*, vol. 2, no. 1, pp. 82–84, 2011. - G. Papaschinopoulos and C. J. Schinas, “On the behavior of the solutions of a system of two nonlinear difference equations,”
*Communications on Applied Nonlinear Analysis*, vol. 5, no. 2, pp. 47–59, 1998. View at Zentralblatt MATH · View at MathSciNet - G. Papaschinopoulos and C. J. Schinas, “Invariants for systems of two nonlinear difference equations,”
*Differential Equations and Dynamical Systems*, vol. 7, no. 2, pp. 181–196, 1999. View at Zentralblatt MATH · View at MathSciNet - G. Papaschinopoulos, J. Schinas, and V. Hatzifilippidis, “Global behavior of the solutions of a max-equation and of a system of two max-equations,”
*Journal of Computational Analysis and Applications*, vol. 5, no. 2, pp. 237–254, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - S. Stević, “A global convergence results with applications to periodic solutions,”
*Indian Journal of Pure and Applied Mathematics*, vol. 33, no. 1, pp. 45–53, 2002. View at MathSciNet - S. Stević, “On the recursive sequence ${x}_{n+1}={\alpha}_{n}+{x}_{n-1}/{x}_{n}$ II,”
*Dynamics of Continuous, Discrete & Impulsive Systems A*, vol. 10, no. 6, pp. 911–916, 2003. View at MathSciNet - S. Stević, “A short proof of the Cushing-Henson conjecture,”
*Discrete Dynamics in Nature and Society*, vol. 2006, Article ID 37264, 5 pages, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - S. Stević, “Global stability of a difference equation with maximum,”
*Applied Mathematics and Computation*, vol. 210, no. 2, pp. 525–529, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - S. Stević, “Periodicity of max difference equations,”
*Utilitas Mathematica*, vol. 83, pp. 69–71, 2010. View at Zentralblatt MATH · View at MathSciNet - S. Stević, “Periodicity of a class of nonautonomous max-type difference equations,”
*Applied Mathematics and Computation*, vol. 217, no. 23, pp. 9562–9566, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - S. Stević, “On some periodic systems of max-type difference equations,”
*Applied Mathematics and Computation*, vol. 218, no. 23, pp. 11483–11487, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - N. Touafek and E. M. Elsayed, “On the periodicity of some systems of nonlinear difference equations,”
*Bulletin Mathématique de la Société des Sciences Mathématiques de Roumanie. Nouvelle Série*, vol. 55, no. 2, pp. 217–224, 2012. View at Zentralblatt MATH · View at MathSciNet - H. Levy and F. Lessman,
*Finite Difference Equations*, Macmillan, New York, NY, USA, 1961. View at MathSciNet - R. C. Lyness, “Notes 1581,”
*The Mathematical Gazette*, vol. 26, p. 62, 1942. - R. C. Lyness, “Notes 1847,”
*The Mathematical Gazette*, vol. 29, p. 231, 1945. - R. C. Lyness, “Notes 2952,”
*The Mathematical Gazette*, vol. 45, p. 201, 1961.