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Adaptive synchronization of a hyperchaotic system with uncertain parameter

Author

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  • Elabbasy, E.M.
  • Agiza, H.N.
  • El-Dessoky, M.M.

Abstract

This paper addresses the synchronization problem of two Lü hyperchaotic dynamical systems in the presence of unknown system parameters. Based on Lyapunov stability theory an adaptive control law is derived to make the states of two identical Lü hyperchaotic systems with unknown system parameters asymptotically synchronized. Numerical simulations are presented to show the effectiveness of the proposed chaos synchronization schemes.

Suggested Citation

  • Elabbasy, E.M. & Agiza, H.N. & El-Dessoky, M.M., 2006. "Adaptive synchronization of a hyperchaotic system with uncertain parameter," Chaos, Solitons & Fractals, Elsevier, vol. 30(5), pages 1133-1142.
    • Handle: RePEc:eee:chsofr:v:30:y:2006:i:5:p:1133-1142
    DOI: 10.1016/j.chaos.2005.09.047
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    Cited by:

    1. Yang, Li-Xin & Chu, Yan-Dong & Zhang, Jian-Gang & Li, Xian-Feng, 2009. "Chaos synchronization of coupled hyperchaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 724-730.
    2. Xu, Yuhua & Zhou, Wuneng & Fang, Jian-an, 2009. "Hybrid dislocated control and general hybrid projective dislocated synchronization for the modified Lü chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1305-1315.
    3. Ge, Zheng-Ming & Yang, Cheng-Hsiung, 2009. "Chaos synchronization and chaotization of complex chaotic systems in series form by optimal control," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 994-1002.
    4. Chen, Mou & Chen, Wen-hua, 2009. "Robust adaptive neural network synchronization controller design for a class of time delay uncertain chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2716-2724.
    5. Elabbasy, E.M. & El-Dessoky, M.M., 2008. "Synchronization of van der Pol oscillator and Chen chaotic dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1425-1435.
    6. Ge, Zheng-Ming & Chang, Ching-Ming, 2009. "Nonlinear generalized synchronization of chaotic systems by pure error dynamics and elaborate nondiagonal Lyapunov function," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1959-1974.
    7. Yang, Li-Xin & Chu, Yan-Dong & Zhang, Jian-Gang & Li, Xian-Feng & Chang, Ying-Xiang, 2009. "Chaos synchronization in autonomous chaotic system via hybrid feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 214-223.
    8. Koronovskii, Alexey A. & Moskalenko, Olga I. & Ponomarenko, Vladimir I. & Prokhorov, Mikhail D. & Hramov, Alexander E., 2016. "Binary generalized synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 133-139.

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