IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v58y2014icp22-26.html
   My bibliography  Save this article

Robust synchronization of FitzHugh–Nagumo network with parameter disturbances by sliding mode control

Author

Listed:
  • Zhang, Qunjiao

Abstract

In this paper, based on the sliding mode control method, the robust synchronization for a coupled FitzHugh–Nagumo (FHN) neurobiological network with parameter disturbances is investigated. Some theoretical criteria are derived to realize the robust synchronization of the FHN network with disturbed parameters, and the synchronization occurs without dependence on the type and magnitude of the noise, which greatly extend some existing results for two or three coupled FHN neurons. Finally, a numerical example is given to illustrate the effectiveness of the proposed theoretical results.

Suggested Citation

  • Zhang, Qunjiao, 2014. "Robust synchronization of FitzHugh–Nagumo network with parameter disturbances by sliding mode control," Chaos, Solitons & Fractals, Elsevier, vol. 58(C), pages 22-26.
    • Handle: RePEc:eee:chsofr:v:58:y:2014:i:c:p:22-26
    DOI: 10.1016/j.chaos.2013.11.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077913002051
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2013.11.002?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. Kaiyu Liu & Zhengqiu Zhang & Liping Wang, 2012. "Existence and Global Exponential Stability of Periodic Solution to Cohen-Grossberg BAM Neural Networks with Time-Varying Delays," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-21, May.
    2. Mou, Chen & Jiang, Chang-sheng & Bin, Jiang & Wu, Qing-xian, 2009. "Sliding mode synchronization controller design with neural network for uncertain chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1856-1863.
    3. 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.
    4. Yu, Haitao & Wang, Jiang & Liu, Qiuxiang & Sun, Jianbing & Yu, Haifeng, 2013. "Delay-induced synchronization transitions in small-world neuronal networks with hybrid synapses," Chaos, Solitons & Fractals, Elsevier, vol. 48(C), pages 68-74.
    5. Courbage, M. & Maslennikov, O.V. & Nekorkin, V.I., 2012. "Synchronization in time-discrete model of two electrically coupled spike-bursting neurons," Chaos, Solitons & Fractals, Elsevier, vol. 45(5), pages 645-659.
    6. He, Yong & Wang, Qing-Guo & Zheng, Wei-Xing, 2005. "Global robust stability for delayed neural networks with polytopic type uncertainties," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1349-1354.
    7. Nguyen, Le Hoa & Hong, Keum-Shik, 2011. "Synchronization of coupled chaotic FitzHugh–Nagumo neurons via Lyapunov functions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(4), pages 590-603.
    8. Wang, Qingyun & Lu, Qishao & Chen, GuanRong & feng, Zhaosheng & Duan, LiXia, 2009. "Bifurcation and synchronization of synaptically coupled FHN models with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 918-925.
    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, Jing & Ye, Weijie & Liu, Shenquan & Lu, Bo & Jiang, Xiaofang, 2016. "Qualitative and quantitative aspects of synchronization in coupled CA1 pyramidal neurons," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 32-38.
    2. Mbeunga, N.K. & Nana, B. & Woafo, P., 2021. "Dynamics of array mechanical arms coupled each to a Fitzhugh-Nagumo neuron," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    3. 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.
    4. Yu, Haitao & Wang, Jiang & Liu, Chen & Deng, Bin & Wei, Xile, 2014. "Delay-induced synchronization transitions in modular scale-free neuronal networks with hybrid electrical and chemical synapses," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 405(C), pages 25-34.
    5. Yu, Dong & Wu, Yong & Yang, Lijian & Zhao, Yunjie & Jia, Ya, 2023. "Effect of topology on delay-induced multiple resonances in locally driven systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).
    6. Chen, Mou & Chen, Wen-hua, 2009. "Robust adaptive neural network synchronization controller design for a class of time delay uncertain chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2716-2724.
    7. Singh, Vimal, 2007. "Some remarks on global asymptotic stability of neural networks with constant time delay," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1720-1724.
    8. Singh, Vimal, 2007. "Global asymptotic stability of neural networks with delay: Comparative evaluation of two criteria," Chaos, Solitons & Fractals, Elsevier, vol. 31(5), pages 1187-1190.
    9. Li, Chuandong & Chen, Jinyu & Huang, Tingwen, 2007. "A new criterion for global robust stability of interval neural networks with discrete time delays," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 561-570.
    10. Lu, Junwei & Guo, Yiqian & Xu, Shengyuan, 2006. "Global asymptotic stability analysis for cellular neural networks with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 29(2), pages 349-353.
    11. Singh, Vimal, 2007. "Simplified approach to the exponential stability of delayed neural networks with time varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 609-616.
    12. Gau, R.S. & Lien, C.H. & Hsieh, J.G., 2007. "Global exponential stability for uncertain cellular neural networks with multiple time-varying delays via LMI approach," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1258-1267.
    13. Gong, Yubing & Xie, Yanhang & Lin, Xiu & Hao, Yinghang & Ma, Xiaoguang, 2010. "Ordering chaos and synchronization transitions by chemical delay and coupling on scale-free neuronal networks," Chaos, Solitons & Fractals, Elsevier, vol. 43(1), pages 96-103.
    14. Zhang, Chunrui & Zhang, Xianhong & Zhang, Yazhou, 2018. "Dynamic properties of feed-forward neural networks and application in contrast enhancement for image," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 281-290.
    15. You, Surong & Hu, Liangjian & Mao, Wei & Mao, Xuerong, 2015. "Robustly exponential stabilization of hybrid uncertain systems by feedback controls based on discrete-time observations," Statistics & Probability Letters, Elsevier, vol. 102(C), pages 8-16.
    16. Singh, Vimal, 2007. "Novel LMI condition for global robust stability of delayed neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 503-508.
    17. Mak, K.L. & Peng, J.G. & Xu, Z.B. & Yiu, K.F.C., 2007. "A new stability criterion for discrete-time neural networks: Nonlinear spectral radius," Chaos, Solitons & Fractals, Elsevier, vol. 31(2), pages 424-436.
    18. Singh, Vimal, 2006. "New global robust stability results for delayed cellular neural networks based on norm-bounded uncertainties," Chaos, Solitons & Fractals, Elsevier, vol. 30(5), pages 1165-1171.
    19. Wang, Jing & Liu, Shenquan & Liu, Xuanliang, 2014. "Quantification of synchronization phenomena in two reciprocally gap-junction coupled bursting pancreatic β-cells," Chaos, Solitons & Fractals, Elsevier, vol. 68(C), pages 65-71.
    20. Gong, Yubing & Wang, Li & Xu, Bo, 2012. "Delay-induced diversity of firing behavior and ordered chaotic firing in adaptive neuronal networks," Chaos, Solitons & Fractals, Elsevier, vol. 45(4), pages 548-553.

    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:58:y:2014:i:c:p:22-26. 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.