IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v39y2009i3p1335-1345.html
   My bibliography  Save this article

Unidirectional synchronization of Hodgkin–Huxley neurons exposed to ELF electric field

Author

Listed:
  • Wang, Jiang
  • Che, Yan-Qiu
  • Zhou, Si-Si
  • Deng, Bin

Abstract

In this paper, a hybrid control strategy, H∞ variable universe adaptive fuzzy control, is derived and applied to synchronize two Hodgkin–Huxley (HH) neurons exposed to external electric field. Firstly, the modified model of HH neuron exposed to extremely low frequency (ELF) external electric field is established and its periodic and chaotic dynamics in response to sinusoidal electric field stimulation are described. And then the statement of the problem for unidirectional synchronization of two HH neurons is given. Finally H∞ variable universe adaptive fuzzy control is designed to synchronize the HH systems and the simulation results demonstrate the effectiveness of the proposed control method.

Suggested Citation

  • Wang, Jiang & Che, Yan-Qiu & Zhou, Si-Si & Deng, Bin, 2009. "Unidirectional synchronization of Hodgkin–Huxley neurons exposed to ELF electric field," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1335-1345.
    • Handle: RePEc:eee:chsofr:v:39:y:2009:i:3:p:1335-1345
    DOI: 10.1016/j.chaos.2007.05.016
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S096007790700392X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2007.05.016?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Cornejo-Pérez, Octavio & Femat, Ricardo, 2005. "Unidirectional synchronization of Hodgkin–Huxley neurons," Chaos, Solitons & Fractals, Elsevier, vol. 25(1), pages 43-53.
    2. 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.
    3. Xie, Lingli & Teo, Kok-lay & Zhao, Yi, 2007. "Chaos synchronization for continuous chaotic systems by inertial manifold approach," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 234-245.
    4. Wang, Jiang & Deng, Bin & Fei, Xiangyang, 2006. "Chaotic synchronization of two coupled neurons via nonlinear control in external electrical stimulation," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1272-1278.
    5. Yu, Hongjie & Peng, Jianhua, 2006. "Chaotic synchronization and control in nonlinear-coupled Hindmarsh–Rose neural systems," Chaos, Solitons & Fractals, Elsevier, vol. 29(2), pages 342-348.
    6. Czołczynski, K. & Perlikowski, P. & Stefański, A. & Kapitaniak, T., 2007. "Synchronization of self-excited oscillators suspended on elastic structure," Chaos, Solitons & Fractals, Elsevier, vol. 32(3), pages 937-943.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wang, Jiang & Chen, Lisong & Deng, Bin, 2009. "Synchronization of Ghostburster neuron in external electrical stimulation via H∞ variable universe fuzzy adaptive control," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2076-2085.
    2. Wang, Jiang & Zhang, Ting & Che, Yanqiu, 2007. "Chaos control and synchronization of two neurons exposed to ELF external electric field," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 839-850.
    3. Che, Yan-Qiu & Wang, Jiang & Zhou, Si-Si & Deng, Bin, 2009. "Robust synchronization control of coupled chaotic neurons under external electrical stimulation," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1333-1342.
    4. Ji, J.C. & Zhang, N., 2009. "Nonlinear response of a forced van der Pol–Duffing oscillator at non-resonant bifurcations of codimension two," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1467-1475.
    5. Qin, Weiyang & Yang, Yongfen & Kang, Zhaohui & Ren, Xingmin, 2009. "Controlling chaos and response of dynamical system by synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1466-1473.
    6. Wang, Jiang & Deng, Bin & Fei, Xiangyang, 2008. "Synchronization of chaotic neurons coupled with gap junction with time delays in external electrical stimulation," Chaos, Solitons & Fractals, Elsevier, vol. 35(3), pages 512-518.
    7. He, Ji-Huan, 2006. "A modified Hodgkin–Huxley model," Chaos, Solitons & Fractals, Elsevier, vol. 29(2), pages 303-306.
    8. Branislav Rehák & Volodymyr Lynnyk, 2021. "Synchronization of a Network Composed of Stochastic Hindmarsh–Rose Neurons," Mathematics, MDPI, vol. 9(20), pages 1-16, October.
    9. Sun, Li & Wang, Jiang & Deng, Bin, 2009. "Global synchronization of two Ghostburster neurons via active control," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1213-1220.
    10. Bonacini, E. & Burioni, R. & di Volo, M. & Groppi, M. & Soresina, C. & Vezzani, A., 2016. "How single node dynamics enhances synchronization in neural networks with electrical coupling," Chaos, Solitons & Fractals, Elsevier, vol. 85(C), pages 32-43.
    11. Maganti, Ganesh B. & Singh, Sahjendra N., 2006. "Output feedback form of Chua’s circuit and modular adaptive control of chaos using single measurement," Chaos, Solitons & Fractals, Elsevier, vol. 28(3), pages 724-738.
    12. 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.
    13. Burić, Nikola & Todorović, Kristina & Vasović, Nebojša, 2009. "Exact synchronization of noisy bursting neurons with coupling delays," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1127-1135.
    14. Wang, Jiang & Zhang, Ting & Deng, Bin, 2007. "Synchronization of FitzHugh–Nagumo neurons in external electrical stimulation via nonlinear control," Chaos, Solitons & Fractals, Elsevier, vol. 31(1), pages 30-38.
    15. Zheng, G. & Boutat, D. & Floquet, T. & Barbot, J.P., 2009. "Secure communication based on multi-input multi-output chaotic system with large message amplitude," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1510-1517.
    16. 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.
    17. Jia, Chenhui & Wang, Jiang & Deng, Bin, 2009. "How the self-coupled neuron can affect the chaotic synchronization of network," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1112-1119.
    18. Che, Yan-Qiu & Wang, Jiang & Zhou, Si-Si & Deng, Bin, 2009. "Synchronization control of Hodgkin–Huxley neurons exposed to ELF electric field," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1588-1598.
    19. Li, Demin & Wang, Zidong & Zhou, Jie & Fang, Jian’an & Ni, Jinjin, 2008. "A note on chaotic synchronization of time-delay secure communication systems," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 1217-1224.
    20. Hou, Zhangliang & Ma, Jun & Zhan, Xuan & Yang, Lijian & Jia, Ya, 2021. "Estimate the electrical activity in a neuron under depolarization field," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:39:y:2009:i:3:p:1335-1345. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.