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Discrete Dynamics in Nature and Society
Volume 2011 (2011), Article ID 437156, 19 pages
http://dx.doi.org/10.1155/2011/437156
Research Article

Generalized Projective Synchronization for Different Hyperchaotic Dynamical Systems

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

Received 14 July 2011; Accepted 24 August 2011

Academic Editor: Recai Kilic

Copyright © 2011 M. M. El-Dessoky and E. Saleh. 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. E. Ott, C. Grebogi, and J. Yorke, “Controlling chaos,” Physical Review Letters, vol. 64, no. 11, pp. 1196–1199, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. A. W. Hubler, “Adaptive control of chaotic system,” Helvetica Physica Acta, vol. 62, pp. 343–346, 1989. View at Google Scholar
  3. K. Pyragas, “Continuous control of chaos by self-controlling feedback,” Physics Letters A, vol. 170, no. 6, pp. 421–428, 1992. View at Publisher · View at Google Scholar
  4. G. Chen and X. Dong, “On feedback control of chaotic nonlinear dynamic systems,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 2, no. 2, pp. 407–411, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. G. Chen, “On some controllability conditions for chaotic dynamics control,” Chaos, Solitons and Fractals, vol. 8, no. 9, pp. 1461–1470, 1997. View at Publisher · View at Google Scholar · View at MathSciNet
  6. K. Pyragas, “Control of chaos via extended delay feedback,” Physics Letters. A, vol. 206, no. 5-6, pp. 323–330, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. 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
  8. T. L. Carroll and L. M. Pecora, “Synchronizing a chaotic systems,” IEEE Transactions on Circuits and Systems, vol. 38, no. 4, pp. 453–456, 1991. View at Publisher · View at Google Scholar
  9. J. M. Gonzăalez-Miranda, “Chaotic systems with a null conditional Lyapunov exponent under nonlinear driving,” Physical Review E, vol. 53, no. 1, pp. R5–R8, 1996. View at Publisher · View at Google Scholar
  10. 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 Publisher · View at Google Scholar
  11. L. Zhigang and X. Daolin, “Stability criterion for projective synchronization in three-dimensional chaotic systems,” Physics Letters A, vol. 282, no. 3, pp. 175–179, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. X. Daolin and L. Zhigang, “Controlled projective synchronization in nonpartially-linear chaotic systems,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 12, no. 6, pp. 1395–1402, 2002. View at Publisher · View at Google Scholar
  13. X. Daolin, Ong Wee-leng, and L. Zhigang, “Criteria for the occurrence of projective synchronization in chaotic systems of arbitrary dimension,” Physics Letters A, vol. 305, no. 3-4, pp. 167–172, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. J.-p. Yan and C.-p. Li, “Generalized projective synchronization for the chaotic Lorenz system and the chaotic Chen system,” Journal of Shanghai University, vol. 10, no. 4, pp. 299–304, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. Z.-M. Ge and C.-H. Yang, “The generalized synchronization of a quantum—CNN chaotic oscillator with different order systems,” Chaos, Solitons & Fractals, vol. 35, pp. 980–990, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. J. Liu, S. H. Chen, and J. A. Lu, “Projective synchronization in a unified chaotic system and its control,” Acta Physica Sinica, vol. 52, pp. 1595––1599, 2003. View at Google Scholar
  17. G.-H. Li, “Generalized projective synchronization of two chaotic systems by using active control,” Chaos, Solitons and Fractals, vol. 30, no. 1, pp. 77–82, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. J. H. Park, “Adaptive control for modified projective synchronization of a four—dimensional chaotic system with uncertain parameters,” Journal of Computational and Applied Mathematics, vol. 213, pp. 288–293, 2008. View at Publisher · View at Google Scholar
  19. Z.-M. Ge and G.-H. Lin, “The complete, lag and anticipated synchronization of a BLDCM chaotic system,” Chaos, Solitons and Fractals, vol. 34, no. 3, pp. 740–764, 2007. View at Publisher · View at Google Scholar
  20. N. F. Rulkov, M. M. Sushchik, L. S. Tsimring, and H. D. 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
  21. Y. L. Zou and J. Zhu, “Controlling projective synchronizationin coupled chaotic systems,” Chinese Physics, vol. 15, no. 9, pp. 1965––1970, 2006. View at Google Scholar
  22. L. Kocarev and U. Parlitz, “Synchrionizing spatiotemporal chaos in coupled nonlinear oscillators,” Physical Review Letters, vol. 77, pp. 2206–2209, 1996. View at Publisher · View at Google Scholar
  23. H. D. I. Abarbanel, N. F. Rulkov, and M. M. Sushchik, “Generalized synchronization of chaos: the auxiliary system approach,” Physical Review E, vol. 53, pp. 4528–4535, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  24. D. Huang, “Simple adaptive feedback controller for identical chaos synchronization,” Physical Review E, vol. 71, pp. 37–203, 2005. View at Google Scholar
  25. D. Huang, “Adaptive-feedback control algorithm,” Physical Review E, vol. 73, no. 6, pp. 66–204, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  26. M. Hu and Z. Xu, “Adaptive feedback controller for projective synchronization,” Nonlinear Analysis, vol. 9, no. 3, pp. 1253–1260, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  27. J. Cao and J. Lu, “Adaptive synchronization of neural networks with or without time-varying delay,” Chaos, vol. 16, no. 1, pp. 13–101, 2006. View at Publisher · View at Google Scholar · View at PubMed · View at Zentralblatt MATH · View at MathSciNet
  28. M. Chen and D. Zhou, “Synchronization in uncertain complex networks,” Chaos, vol. 16, no. 1, pp. 13–101, 2006. View at Publisher · View at Google Scholar · View at PubMed · View at Zentralblatt MATH · View at MathSciNet
  29. 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 Zentralblatt MATH
  30. X. Wang and M. Wan, “A hyper chaos generated from Lorenz system,” Physica A, vol. 387, pp. 3751––3758, 2008. View at Google Scholar
  31. Y. Li, W. K. S. Tang, and G. Chen, “Hyperchaos evolved from the generalized Lorenz equation,” International Journal of Circuit Theory and Applications, vol. 33, no. 4, pp. 235–251, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  32. A. Chen, J. Lu, J. Lü, and S. Yu, “Generating hyperchaotic Lü attractor via state feedback control,” Physics A, vol. 364, pp. 103–110, 2006. View at Publisher · View at Google Scholar