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Mathematical Problems in Engineering
Volume 2012, Article ID 810626, 16 pages
http://dx.doi.org/10.1155/2012/810626
Research Article

Adaptive Modified Function Projective Synchronization between Two Different Hyperchaotic Dynamical Systems

1Department of Mathematics, Faculty of Science, King AbdulAziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

Received 11 November 2011; Accepted 17 December 2011

Academic Editor: Jun-Juh Yan

Copyright © 2012 M. M. El-Dessoky 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
  2. M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, “Phase synchronization of chaotic oscillators,” Physical Review Letters, vol. 76, no. 11, pp. 1804–1807, 1996. View at Google Scholar · View at Scopus
  3. N. F. Rulkov, M. M. Sushchik, L. S. Tsimring, and H. D. I. Abarbanel, “Generalized synchronization of chaos in directionally coupled chaotic systems,” Physical Review E, vol. 51, no. 2, pp. 980–994, 1995. View at Publisher · View at Google Scholar · View at Scopus
  4. M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, “From phase to lag synchronization in coupled chaotic oscillators,” Physical Review Letters, vol. 78, no. 22, pp. 4193–4196, 1997. View at Google Scholar · View at Scopus
  5. S. Boccaletti and D. L. Valladares, “Characterization of intermittent lag synchronization,” Physical Review E, vol. 62, no. 5 B, pp. 7497–7500, 2000. View at Google Scholar · View at Scopus
  6. A. E. Hramov and A. A. Koronovskii, “An approach to chaotic synchronization,” Chaos, vol. 14, no. 3, pp. 603–610, 2004. View at Publisher · View at Google Scholar
  7. A. E. Hramov, A. A. Koronovskii, and O. I. Moskalenko, “Generalized synchronization onset,” Europhysics Letters, vol. 72, no. 6, pp. 901–907, 2005. View at Publisher · View at Google Scholar
  8. R. Mainieri and J. Rehacek, “Projective synchronization in three-dimensional chaotic systems,” Physical Review Letters, vol. 82, no. 15, pp. 3042–3045, 1999. View at Google Scholar · View at Scopus
  9. G. H. Li, “Generalized projective synchronization between Lorenz system and Chen's system,” Chaos, Solitons and Fractals, vol. 32, no. 4, pp. 1454–1458, 2007. View at Publisher · View at Google Scholar · View at Scopus
  10. G.-H. Li, “Modified projective synchronization of chaotic system,” Chaos, Solitons and Fractals, vol. 32, no. 5, pp. 1786–1790, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. L. Runzi, “Adaptive function project synchronization of Rössler hyperchaotic system with uncertain parameters,” Physics Letters A, vol. 372, no. 20, pp. 3667–3671, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. H. Du, Q. Zeng, and C. Wang, “Function projective synchronization of different chaotic systems with uncertain parameters,” Physics Letters A, vol. 372, no. 33, pp. 5402–5410, 2008. View at Publisher · View at Google Scholar · View at Scopus
  13. M. T. Yassen, “Adaptive control and synchronization of a modified Chua's circuit system,” Applied Mathematics and Computation, vol. 135, no. 1, pp. 113–128, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. Z. Li, C. Han, and S. Shi, “Modification for synchronization of Rössler and Chen chaotic systems,” Physics Letters A, vol. 301, no. 3-4, pp. 224–230, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. Y. Wang, Z.-H. Guan, and H. O. Wang, “Feedback and adaptive control for the synchronization of Chen system via a single variable,” Physics Letters A, vol. 312, no. 1-2, pp. 34–40, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. J. Huang, “Adaptive synchronization between different hyperchaotic systems with fully uncertain parameters,” Physics Letters A, vol. 372, no. 27-28, pp. 4799–4804, 2008. View at Publisher · View at Google Scholar · View at Scopus
  17. D. Huang, “Stabilizing near-nonhyperbolic chaotic systems with applications,” Physical Review Letters, vol. 93, no. 21, Article ID 214101, 2004. View at Publisher · View at Google Scholar · View at Scopus
  18. D. Huang, “Simple adaptive-feedback controller for identical chaos synchronization,” Physical Review E, vol. 71, no. 3, Article ID 037203, pp. 1–4, 2005. View at Publisher · View at Google Scholar · View at Scopus
  19. D. Huang, “Adaptive-feedback control algorithm,” Physical Review E, vol. 73, no. 6, article 066204, p. 8, 2006. View at Publisher · View at Google Scholar
  20. Q. Jia, “Hyperchaos generated from the Lorenz chaotic system and its control,” Physics Letters A, vol. 366, no. 3, pp. 217–222, 2007. View at Publisher · View at Google Scholar · View at Scopus
  21. X. Wang and M. Wang, “A hyperchaos generated from Lorenz system,” Physica A, vol. 387, no. 14, pp. 3751–3758, 2008. View at Publisher · View at Google Scholar
  22. T. Gao, G. Chen, Z. Chen, and S. Cang, “The generation and circuit implementation of a new hyper-chaos based upon Lorenz system,” Physics Letters A, vol. 361, no. 1-2, pp. 78–86, 2007. View at Publisher · View at Google Scholar · View at Scopus
  23. Y. Li, W. K. S. Tang, and G. Chen, “Generating hyperchaos via state feedback control,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 15, no. 10, pp. 3367–3375, 2005. View at Publisher · View at Google Scholar · View at Scopus
  24. Z. Yan, “Controlling hyperchaos in the new hyperchaotic Chen system,” Applied Mathematics and Computation, vol. 168, no. 2, pp. 1239–1250, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH