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Adaptive synchronization of unidirectional and mutual coupled chaotic systems

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  • Ge, Zheng-Ming
  • Chen, Yen-Sheng

Abstract

Two theorems for adaptive synchronization of unidirectional and mutual coupled nonautonomous chaotic systems are derived individually. An adaptive coupling gain is realized by adopting an adaptive law to estimate the Lipschitz constant of the chaotic system. The Lorenz system and the Duffing system are simulated to illustrate theoretical results for unidirectional and mutual coupled chaotic systems, respectively.

Suggested Citation

  • Ge, Zheng-Ming & Chen, Yen-Sheng, 2005. "Adaptive synchronization of unidirectional and mutual coupled chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 881-888.
    • Handle: RePEc:eee:chsofr:v:26:y:2005:i:3:p:881-888
    DOI: 10.1016/j.chaos.2005.01.052
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    References listed on IDEAS

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    1. Lin, Jui-Sheng & Yan, Jun-Juh & Liao, Teh-Lu, 2005. "Chaotic synchronization via adaptive sliding mode observers subject to input nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 24(1), pages 371-381.
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    Cited by:

    1. Ge, Zheng-Ming & Hsu, Mao-Yuan, 2008. "Chaos excited chaos synchronizations of integral and fractional order generalized van der Pol systems," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 592-604.
    2. Ge, Zheng-Ming & Ou, Chan-Yi, 2008. "Chaos synchronization of fractional order modified duffing systems with parameters excited by a chaotic signal," Chaos, Solitons & Fractals, Elsevier, vol. 35(4), pages 705-717.
    3. 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.
    4. Ge, Zheng-Ming & Chen, Yen-Sheng, 2007. "Synchronization of mutual coupled chaotic systems via partial stability theory," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 787-794.
    5. Ge, Zheng-Ming & Lin, Guo-Hua, 2007. "The complete, lag and anticipated synchronization of a BLDCM chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 740-764.
    6. Hu, Wuhua & Wang, Jiang & Li, Xiumin, 2009. "An approach of partial control design for system control and synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1410-1417.
    7. Ge, Zheng-Ming & Jhuang, Wei-Ren, 2007. "Chaos, control and synchronization of a fractional order rotational mechanical system with a centrifugal governor," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 270-289.
    8. 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.
    9. Chen, Juhn-Horng & Chen, Hsien-Keng & Lin, Yu-Kai, 2009. "Synchronization and anti-synchronization coexist in Chen–Lee chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 707-716.
    10. Ge, Zheng-Ming & Zhang, An-Ray, 2007. "Chaos in a modified van der Pol system and in its fractional order systems," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1791-1822.
    11. Pengyu Li & Juan Du & Shouliang Li & Yazhao Zheng & Bowen Jia, 2019. "The Synchronization of N Cascade-Coupled Chaotic Systems," Complexity, Hindawi, vol. 2019, pages 1-10, December.
    12. Ge, Zheng-Ming & Hsu, Mao-Yuan, 2007. "Chaos in a generalized van der Pol system and in its fractional order system," Chaos, Solitons & Fractals, Elsevier, vol. 33(5), pages 1711-1745.

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