Hybrid Synchronization of a Chen Hyper-Chaotic System with Two Simple Linear Feedback Controllers

DOI: 10.4236/am.2013.411A2003   PDF   HTML     2,904 Downloads   4,304 Views   Citations


This paper brings attention on the hybrid synchronization of the Chen hyper-chaotic system by using some simple controllers. We give the sufficient conditions for achieving the goal by using the Lyapunov stability theory, and we verify our conclusion by numerical simulations.

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G. Xu and S. Chen, "Hybrid Synchronization of a Chen Hyper-Chaotic System with Two Simple Linear Feedback Controllers," Applied Mathematics, Vol. 4 No. 11B, 2013, pp. 13-17. doi: 10.4236/am.2013.411A2003.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] T. Y. Li and J. A. Yorke, “Period Three Implies Chaos,” The American Mathematical Monthly, Vol. 82, No. 10. 1975, pp. 985-992. http://dx.doi.org/10.2307/2318254
[2] E. Rodriguez, N. George, J. P. Lachaux, J. Martinerie, B. Renault and F. J. Varela, “Perception’s Shadow: LongDistance Synchronization of Human Brain Activity,” Nature, Vol. 397, No. 6718, 1999, pp. 430-433.
[3] R. Yoshida, M. Tanaka, S. Onodera, T. Yamaguchi and E. Kokufuta, “In-Phase Synchronization of Chemical and Mechanical Oscillations in Self-Oscillating Gels,” The Journal of Physical Chemistry A, Vol. 104, No. 32, 2000, pp. 7549-7555. http://dx.doi.org/10.1021/jp0011600
[4] W. Singer, “Synchronization of Cortical Activity and Its Putative Role in Information Processing and Learning,” Annual Review of Physiology, Vol. 55, No. 1, 1993, pp. 349-374.
[5] L. M. Pecora and T. L. Carroll, “Synchronization in Chaotic Systems,” Physical Review Letters, Vol. 64, No. 8, 1990, pp. 821-824.
[6] S. Boccaletti, J. Kurths, G. Osipov, D. L. Valladares and C. S. Zhou, “The Synchronization of Chaotic Systems,” Physics Reports, Vol. 366, No. 1, 2002, pp. 1-101.
[7] M. G. Rosenblum, A. S. Pikovsky and J. Kurths, “Phase Synchronization of Chaotic Oscillators,” Physical Review Letters, Vol. 76, No. 11, 1996, pp. 1804-1807.
[8] R. Mainieri and J. Rehacek, “Projective Synchronization in Three-Dimensional Chaotic Systems,” Physical Review Letters, Vol. 82, No. 15, 1999, pp. 3042-3045.
[9] C. M. Kim, S. Rim, W. H. Kye, J. W. Ryu and Y. J. Park, “Anti-Synchronization of Chaotic Oscillators,” Physics Letters A, Vol. 320, No. 1, 2003, pp. 39-46.
[10] Q. Xie, G. Chen and E. M. Bollt, “Hybrid Chaos Synchro Nization and Its Application in Information Processing,” Mathematical and Computer Modeling, Vol. 35, No. 1, 2002, pp. 145-163.
[11] C. Li, Q. Chen and T. Huang, “Coexistence of Anti-Phase and Complete Synchronization in Coupled Chen System via a Single Variable,” Chaos, Solitons & Fractals, Vol. 38, No. 2, 2008, pp. 461-464.
[12] Q. Zhang, J. Lü and S .Chen, “Coexistence of Anti-Phase and Complete Synchronization in the Generalized Lorenz System,” Communications in Nonlinear Science and Numerical Simulation, Vol. 15, No. 10, 2010, pp. 30673072. http://dx.doi.org/10.1016/j.cnsns.2009.11.020
[13] K. S. Sudheer and M. Sabir, “Hybrid Synchronization of Hyperchaotic Lu System,” Pramana, Vol. 73, No. 4, 2009, pp. 781-786.
[14] Y. Li, W. K. Tang and G. Chen, “Generating Hyperchaos via State Feedback Control,” International Journal of Bifurcation and Chaos, Vol. 15, No. 10, 2005, pp. 33673375.
[15] F. Zhang, “The Schur Complement and Its Applications,” Springer Science & Business Media, Inc., Boston, 2005.

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