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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 981503, 8 pages
http://dx.doi.org/10.1155/2013/981503
Research Article

Generalized Synchronization of Stochastic Discrete Chaotic System with Poisson Distribution Coefficient

School of Information and Computation Science, Beifang University of Nationalities, Yinchuan 750021, China

Received 29 March 2013; Revised 10 June 2013; Accepted 1 July 2013

Academic Editor: Gualberto Solís-Perales

Copyright © 2013 Shao-juan Ma 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

  1. L. M. Pecora and T. L. Carroll, “Synchronization in chaotic systems,” Physical Review Letters, vol. 64, no. 8, pp. 821–824, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. G. Chen and X. Dong, From Chaos to Order Methodologies, Perspectives and Applications, with a Foreword by Alistair Mees, vol. 24 of World Scientific Series on Nonlinear Science. Series A: Monographs and Treatises, World Scientific Publishing, River Edge, NJ, USA, 1998. View at MathSciNet
  3. H. Taghvafard and G. H. Erjaee, “Phase and anti-phase synchronization of fractional order chaotic systems via active control,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 10, pp. 4079–4088, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. D. Yu and U. Parlitz, “Partial synchronization of chaotic systems with uncertainty,” Physical Review E, vol. 77, no. 6, Article ID 066208, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  5. B. Xin, T. Chen, and Y. Liu, “Projective synchronization of chaotic fractional-order energy resources demand-supply systems via linear control,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 11, pp. 4479–4486, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. H. Du, P. Shi, and N. Lü, “Function projective synchronization in complex dynamical networks with time delay via hybrid feedback control,” Nonlinear Analysis: Real World Applications, vol. 14, no. 2, pp. 1182–1190, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. H.-G. Zhang, T.-D. Ma, J. Fu, and S.-C. Tong, “Robust lag synchronization between two different chaotic systems via dual-stage impulsive control,” Chinese Physics B, vol. 18, no. 9, pp. 3751–3757, 2009. View at Publisher · View at Google Scholar · View at Scopus
  8. Y. Chenggui, Z. Qi, and Y. Jun, “Complete synchronization induced by disorder in coupled chaotic lattices,” Physics Letters A, vol. 377, no. 5, pp. 370–377, 2013.
  9. J. Zhao and T. Ren, “Q-S synchronization between chaotic systems with double scaling functions,” Nonlinear Dynamics, vol. 62, no. 3, pp. 665–672, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. S. Cheng, J. C. Ji, and J. Zhou, “Fast synchronization of directionally coupled chaotic systems,” Applied Mathematical Modelling, vol. 37, no. 1-2, pp. 127–136, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  11. X. Wan and J. Sun, “Adaptive-impulsive synchronization of chaotic systems,” Mathematics and Computers in Simulation, vol. 81, no. 8, pp. 1609–1617, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. M. Peng, E.-W. Bai, and K. E. Lonngren, “On the synchronization of delay discrete models,” Chaos, Solitons and Fractals, vol. 22, no. 3, pp. 573–576, 2004. View at Publisher · View at Google Scholar · View at Scopus
  13. G. Baier and M. Klein, “Maximum hyperchaos in generalized Hénon maps,” Physics Letters A, vol. 151, no. 6-7, pp. 281–284, 1990. View at Publisher · View at Google Scholar · View at MathSciNet
  14. B. Chen and J. Chen, “Bifurcation and chaotic behavior of a discrete singular biological economic system,” Applied Mathematics and Computation, vol. 219, no. 5, pp. 2371–2386, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  15. Z. Zhang and X. Liu, “Observer-based impulsive chaotic synchronization of discrete-time switched systems,” Nonlinear Dynamics, vol. 62, no. 4, pp. 781–789, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. Z.-Y. Wu and X.-C. Fu, “Adaptive function projective synchronization of discrete chaotic systems with unknown parameters,” Chinese Physics Letters, vol. 27, no. 5, Article ID 050502, 2010. View at Publisher · View at Google Scholar · View at Scopus
  17. K. Hengster-Movric, K. You, F. L. Lewis, and L. Xie, “Synchronization of discrete-time multi-agent systems on graphs using Riccati design,” Automatica, vol. 49, no. 2, pp. 414–423, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. W. Liu, Z. Wang, and W. Zhang, “Controlled synchronization of discrete-time chaotic systems under communication constraints,” Nonlinear Dynamics, vol. 69, no. 1-2, pp. 223–230, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. N. Vasegh and V. J. Majd, “Adaptive fuzzy synchronization of discrete-time chaotic systems,” Chaos, Solitons and Fractals, vol. 28, no. 4, pp. 1029–1036, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. H. Su and X. H. Ding, “Synchronization in time-discrete delayed chaotic systems,” Neurocomputing, vol. 73, no. 1–3, pp. 478–483, 2009. View at Publisher · View at Google Scholar · View at Scopus
  21. Z. Yan, “Q-S (complete or anticipated) synchronization backstepping scheme in a class of discrete-time chaotic (hyperchaotic) systems: a symbolic-numeric computation approach,” Chaos, vol. 16, no. 1, Article ID 013119, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  22. H.-L. An and Y. Chen, “The function cascade synchronization scheme for discrete-time hyperchaotic systems,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 4, pp. 1494–1501, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. M. Eisencraft and A. M. Batista, “Discrete-time chaotic systems synchronization performance under additive noise,” Signal Processing, vol. 91, no. 8, pp. 2127–2131, 2011. View at Publisher · View at Google Scholar · View at Scopus
  24. G. Grassi and D. A. Miller, “Dead-beat full state hybrid projective synchronization for chaotic maps using a scalar synchronizing signal,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 4, pp. 1824–1830, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. P. Borwein and T. Erdélyi, Polynomials and Polynomial Inequality, Springer, New York, NY, USA, 1995.