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Adaptive control and synchronization of chaotic systems consisting of Van der Pol oscillators coupled to linear oscillators

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  • Fotsin, Hilaire
  • Bowong, Samuel

Abstract

This paper deals with the problem of control and synchronization of coupled second-order oscillators showing a chaotic behavior. A classical feedback controller is first used to stabilize the system at its equilibrium. An adaptive observer is then designed to synchronize the states of the master and slave oscillators using a single scalar signal corresponding to an observable state variable of the driving oscillator. An interesting feature of the proposed approach is that it can be used for chaos control as well as synchronization purposes. Numerical simulations results confirming the analytical predictions are shown and pspice simulations are also performed to confirm the efficiency of the proposed control scheme.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:27:y:2006:i:3:p:822-835
    DOI: 10.1016/j.chaos.2005.04.055
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    References listed on IDEAS

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    1. 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.
    2. Andrievsky, B., 2002. "Adaptive synchronization methods for signal transmission on chaotic carriers," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 58(4), pages 285-293.
    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.
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    Cited by:

    1. dos Santos Coelho, Leandro & Coelho, Antonio Augusto Rodrigues, 2009. "Model-free adaptive control optimization using a chaotic particle swarm approach," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2001-2009.
    2. Liu, Bo & Wang, Ling & Jin, Yi-Hui & Huang, De-Xian & Tang, Fang, 2007. "Control and synchronization of chaotic systems by differential evolution algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 412-419.
    3. Chen, Chang-Kuo & Lai, Tsung-Wen & Yan, Jun-Juh & Liao, Teh-Lu, 2009. "Synchronization of two chaotic systems: Dynamic compensator approach," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1055-1063.
    4. Salarieh, Hassan & Shahrokhi, Mohammad, 2008. "Adaptive synchronization of two different chaotic systems with time varying unknown parameters," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 125-136.
    5. Zhang, Ting & Wang, Jiang & Fei, Xiangyang & Deng, Bin, 2007. "Synchronization of coupled FitzHugh–Nagumo systems via MIMO feedback linearization control," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 194-202.
    6. 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.
    7. Zhou, Jin & Cheng, Xuhua & Xiang, Lan & Zhang, Yecui, 2007. "Impulsive control and synchronization of chaotic systems consisting of Van der Pol oscillators coupled to linear oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 607-616.
    8. Kuetche Mbe, E.S. & Fotsin, H.B. & Kengne, J. & Woafo, P., 2014. "Parameters estimation based adaptive Generalized Projective Synchronization (GPS) of chaotic Chua’s circuit with application to chaos communication by parametric modulation," Chaos, Solitons & Fractals, Elsevier, vol. 61(C), pages 27-37.
    9. 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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