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Chaos control and synchronization of a modified chaotic system

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  • Sun, Huijing
  • Cao, Hongjun

Abstract

By replacing a quadratic nonlinear term in Lü system with a piecewise linear signum (PWL) function, a new simplified three-dimensional piecewise continuous autonomous system (a modified Lü system) is introduced. The qualitative properties of the modified Lü system are studied. Based on these properties, the feedback control law is applied to suppress chaos to one of the three equilibria. Several different synchronized methods, such as the active control, one way coupling by active control, and the adaptive active control are applied to achieve the state synchronization of two identical modified Lü systems. These results show that after the simplification, the modified Lü system can still keep the basic and typical nonlinear phenomena. Compared with the original Lü system, the modified Lü system has a lot of advantages, by which the modified Lü system can be more easily implemented by theoretical analysis, and more practicable made by secret communications.

Suggested Citation

  • Sun, Huijing & Cao, Hongjun, 2008. "Chaos control and synchronization of a modified chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1442-1455.
    • Handle: RePEc:eee:chsofr:v:37:y:2008:i:5:p:1442-1455
    DOI: 10.1016/j.chaos.2006.10.056
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    References listed on IDEAS

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    1. Li, Guo-Hui, 2005. "Synchronization of chaotic systems with parameter driven by a chaotic signal," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1485-1489.
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    Cited by:

    1. Dadras, Sara & Momeni, Hamid Reza, 2010. "Adaptive sliding mode control of chaotic dynamical systems with application to synchronization," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(12), pages 2245-2257.
    2. Santos Coelho, Leandro dos & de Andrade Bernert, Diego Luis, 2009. "An improved harmony search algorithm for synchronization of discrete-time chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2526-2532.
    3. Zhang, Jianxiong & Tang, Wansheng, 2009. "Analysis and control for a new chaotic system via piecewise linear feedback," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2181-2190.

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