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Discrete Dynamics in Nature and Society
Volume 2006, Article ID 17237, 9 pages
http://dx.doi.org/10.1155/DDNS/2006/17237

On periodic orbits in discrete-time cascade systems

Department of Mathematics and Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China

Received 28 March 2006; Accepted 19 July 2006

Copyright © 2006 Huimin Li and Xiao-Song Yang. 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. R. M. Abu-Saris and Q. M. Al-Hassan, “On global periodicity of difference equations,” Journal of Mathematical Analysis and Applications, vol. 283, no. 2, pp. 468–477, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. R. P. Agarwal, M. Meehan, and D. O'Regan, Fixed Point Theory and Applications, vol. 141 of Cambridge Tracts in Mathematics, Cambridge University Press, Cambridge, 2001. View at Zentralblatt MATH · View at MathSciNet
  3. L. Alsedà and J. Llibre, “Periods for triangular maps,” Bulletin of the Australian Mathematical Society, vol. 47, no. 1, pp. 41–53, 1993. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. F. M. Atici and G. Sh. Guseinov, “Positive periodic solutions for nonlinear difference equations with periodic coefficients,” Journal of Mathematical Analysis and Applications, vol. 232, no. 1, pp. 166–182, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. Y. Chen, “All solutions of a class of difference equations are truncated periodic,” Applied Mathematics Letters, vol. 15, no. 8, pp. 975–979, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. S. Elaydi and R. J. Sacker, “Global stability of periodic orbits of non-autonomous difference equations and population biology,” Journal of Differential Equations, vol. 208, no. 1, pp. 258–273, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. J. Feuer, “Periodic solutions of the Lyness max equation,” Journal of Mathematical Analysis and Applications, vol. 288, no. 1, pp. 147–160, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. J. A. C. Gallas, “On the origin of periodicity in dynamical systems,” Physica A, vol. 283, no. 1-2, pp. 17–23, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  9. H. Li and X.-S. Yang, “A note on discrete-time dynamical systems under periodic perturbation,” Discrete Dynamics in Nature and Society, vol. 2006, Article ID 84697, 5 pages, 2006. View at Publisher · View at Google Scholar
  10. H. D. Voulov, “On the periodic nature of the solutions of the reciprocal difference equation with maximum,” Journal of Mathematical Analysis and Applications, vol. 296, no. 1, pp. 32–43, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. Z. Zhou, “Periodic orbits on discrete dynamical systems,” Computers & Mathematics with Applications, vol. 45, no. 6–9, pp. 1155–1161, 2003. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet