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Adaptive synchronization of a modified and uncertain chaotic Van der Pol-Duffing oscillator based on parameter identification

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  • Fotsin, H.B.
  • Woafo, P.

Abstract

This paper considers the problem of adaptive synchronization and parameter identification of an uncertain chaotic oscillator. Using recent results on adaptive control, we design a controller which enables both the synchronization of two unidirectionally coupled modified Van der Pol-Duffing oscillators and the estimation of unknown parameters of the drive oscillator.

Suggested Citation

  • Fotsin, H.B. & Woafo, P., 2005. "Adaptive synchronization of a modified and uncertain chaotic Van der Pol-Duffing oscillator based on parameter identification," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1363-1371.
    • Handle: RePEc:eee:chsofr:v:24:y:2005:i:5:p:1363-1371
    DOI: 10.1016/j.chaos.2004.09.101
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    Cited by:

    1. Sun, Fengyun & Zhao, Yi & Zhou, Tianshou, 2007. "Identify fully uncertain parameters and design controllers based on synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1677-1682.
    2. Fotsin, Hilaire & Bowong, Samuel, 2006. "Adaptive control and synchronization of chaotic systems consisting of Van der Pol oscillators coupled to linear oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 822-835.
    3. Fotsin, Hilaire & Bowong, Samuel & Daafouz, Jamal, 2005. "Adaptive synchronization of two chaotic systems consisting of modified Van der Pol–Duffing and Chua oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 215-229.
    4. Li, Ruihong & Xu, Wei & Li, Shuang, 2009. "Anti-synchronization on autonomous and non-autonomous chaotic systems via adaptive feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1288-1296.
    5. Chang, Wei-Der, 2006. "Parameter identification of Rossler’s chaotic system by an evolutionary algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 29(5), pages 1047-1053.
    6. Leutcho, Gervais Dolvis & Kengne, Jacques, 2018. "A unique chaotic snap system with a smoothly adjustable symmetry and nonlinearity: Chaos, offset-boosting, antimonotonicity, and coexisting multiple attractors," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 275-293.
    7. Vincent, U.E., 2008. "Synchronization of identical and non-identical 4-D chaotic systems using active control," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 1065-1075.
    8. He, Qie & Wang, Ling & Liu, Bo, 2007. "Parameter estimation for chaotic systems by particle swarm optimization," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 654-661.
    9. Peng, Bo & Liu, Bo & Zhang, Fu-Yi & Wang, Ling, 2009. "Differential evolution algorithm-based parameter estimation for chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2110-2118.
    10. Shen, Liqun & Wang, Mao, 2008. "Robust synchronization and parameter identification on a class of uncertain chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 106-111.
    11. Li, Chaoshun & Zhou, Jianzhong & Xiao, Jian & Xiao, Han, 2012. "Parameters identification of chaotic system by chaotic gravitational search algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 45(4), pages 539-547.
    12. Zhang, Chaolong & Deng, Feiqi & Peng, Yunjian & Zhang, Bo, 2015. "Adaptive synchronization of Cohen–Grossberg neural network with mixed time-varying delays and stochastic perturbation," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 792-801.
    13. Yu, Wenwu & Cao, Jinde, 2007. "Adaptive synchronization and lag synchronization of uncertain dynamical system with time delay based on parameter identification," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(2), pages 467-482.
    14. Guerra, Fábio A. & Coelho, Leandro dos S., 2008. "Multi-step ahead nonlinear identification of Lorenz’s chaotic system using radial basis neural network with learning by clustering and particle swarm optimization," Chaos, Solitons & Fractals, Elsevier, vol. 35(5), pages 967-979.
    15. Ngamsa Tegnitsap, J.V. & Fotsin, H.B. & Megam Ngouonkadi, E.B., 2021. "Magnetic coupling based control of a chaotic circuit: Case of the van der Pol oscillator coupled to a linear circuit," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).

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