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Nonlinear generalized synchronization of chaotic systems by pure error dynamics and elaborate nondiagonal Lyapunov function

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  • Ge, Zheng-Ming
  • Chang, Ching-Ming

Abstract

By applying pure error dynamics and elaborate nondiagonal Lyapunov function, the nonlinear generalized synchronization is studied in this paper. Instead of current mixed error dynamics in which master state variables and slave state variables are presented, the nonlinear generalized synchronization can be obtained by pure error dynamics without auxiliary numerical simulation. The elaborate nondiagonal Lyapunov function is applied rather than current monotonous square sum Lyapunov function deeply weakening the powerfulness of Lyapunov direct method. Both autonomous and nonautonomous double Mathieu systems are used as examples with numerical simulations.

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  • 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.
    • Handle: RePEc:eee:chsofr:v:39:y:2009:i:4:p:1959-1974
    DOI: 10.1016/j.chaos.2007.06.081
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    References listed on IDEAS

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    1. Ge, Zheng-Ming & Yi, Chang-Xian, 2007. "Chaos in a nonlinear damped Mathieu system, in a nano resonator system and in its fractional order systems," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 42-61.
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    Cited by:

    1. Wu, Xiang-Jun & Lu, Hong-Tao, 2011. "Adaptive generalized function projective lag synchronization of different chaotic systems with fully uncertain parameters," Chaos, Solitons & Fractals, Elsevier, vol. 44(10), pages 802-810.

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