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Impulsive control and synchronization of chaotic Hindmarsh–Rose models for neuronal activity

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  • Wu, Quanjun
  • Zhou, Jin
  • Xiang, Lan
  • Liu, Zengrong

Abstract

The issues of impulsive control and synchronization of chaotic Hindmarsh–Rose model are investigated in this paper. Based on impulsive control theory of dynamical systems, some simple yet less conservative criteria ensuring impulsive stabilization and synchronization of the Hindmarsh–Rose models are derived analytically. Furthermore, two numerical results are presented to demonstrate the effectiveness of the proposed control techniques. It is shown that the obtained results should be helpful to understand dynamical mechanism of signal encoding and transduction from information processing of real neuronal activity.

Suggested Citation

  • Wu, Quanjun & Zhou, Jin & Xiang, Lan & Liu, Zengrong, 2009. "Impulsive control and synchronization of chaotic Hindmarsh–Rose models for neuronal activity," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2706-2715.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:5:p:2706-2715
    DOI: 10.1016/j.chaos.2008.10.002
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    References listed on IDEAS

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    1. Zhou, Jin & Chen, Tianping & Xiang, Lan, 2006. "Robust synchronization of delayed neural networks based on adaptive control and parameters identification," Chaos, Solitons & Fractals, Elsevier, vol. 27(4), pages 905-913.
    2. Zhou, Jin & Xiang, Lan & Liu, Zengrong, 2007. "Synchronization in complex delayed dynamical networks with impulsive effects," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 384(2), pages 684-692.
    3. Park, Ju H., 2006. "Synchronization of a class of chaotic dynamic systems with controller gain variations," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1279-1284.
    4. Lei, Youming & Xu, Wei & Shen, Jianwei & Fang, Tong, 2006. "Global synchronization of two parametrically excited systems using active control," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 428-436.
    5. Park, Ju H., 2006. "Chaos synchronization between two different chaotic dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 549-554.
    6. Uçar, Ahmet & Lonngren, Karl E. & Bai, Er-Wei, 2006. "Synchronization of the unified chaotic systems via active control," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1292-1297.
    7. Rabinovich, M.I. & Varona, P. & Torres, J.J. & Huerta, R. & Abarbanel, H.D.I., 1999. "Slow dynamics and regularization phenomena in ensembles of chaotic neurons," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 263(1), pages 405-414.
    8. Zhou, Jin & Xiang, Lan & Liu, Zengrong, 2007. "Global synchronization in general complex delayed dynamical networks and its applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(2), pages 729-742.
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    Cited by:

    1. Yang, Xinsong & Huang, Chuangxia & Zhu, Quanxin, 2011. "Synchronization of switched neural networks with mixed delays via impulsive control," Chaos, Solitons & Fractals, Elsevier, vol. 44(10), pages 817-826.

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