IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v104y2017icp813-826.html
   My bibliography  Save this article

Synchronized nonlinear patterns in electrically coupled Hindmarsh–Rose neural networks with long-range diffusive interactions

Author

Listed:
  • Etémé, Armand S.
  • Tabi, Conrad B.
  • Mohamadou, Alidou

Abstract

Two electrically coupled Hindmarsh–Rose neural networks are considered, each including power-law long-range dispersive interactions. The whole dynamics of the system is reduced to a set of two coupled complex Ginzburg–Landau equations. The linear stability analysis of the plane wave solutions brings about the existence of two dynamical regimes that predict direct and indirect synchronization of the two networks, under the activation of modulational instability. The conditions for the latter to develop are discussed and used to observe numerically the synchronized longtime dynamics of action potentials, under the effect of both long-range intra-coupling and electrical inter-coupling parameters. Mainly, the synchronization criterion depends on the plane wave amplitudes and for some of their values, perfect and partial inter-network synchronization phenomena are observed. It is also found that indirect synchronization between adjacent networks requires local synchronization among neurons of the same fiber. This is discussed based on some further formulation of the synchronization error, additionally to the time series of action potentials. Some spatiotemporal behaviors of the corresponding bursts of spikes are also discussed using coupling parameters.

Suggested Citation

  • Etémé, Armand S. & Tabi, Conrad B. & Mohamadou, Alidou, 2017. "Synchronized nonlinear patterns in electrically coupled Hindmarsh–Rose neural networks with long-range diffusive interactions," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 813-826.
  • Handle: RePEc:eee:chsofr:v:104:y:2017:i:c:p:813-826
    DOI: 10.1016/j.chaos.2017.09.037
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077917304058
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2017.09.037?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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Tabi, Conrad Bertrand, 2018. "Fractional unstable patterns of energy in α−helix proteins with long-range interactions," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 386-391.
    2. Li, Bo & Liang, Houjun & He, Qizhi, 2021. "Multiple and generic bifurcation analysis of a discrete Hindmarsh-Rose model," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    3. Budzinski, R.C. & Boaretto, B.R.R. & Prado, T.L. & Lopes, S.R., 2019. "Temperature dependence of phase and spike synchronization of neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 35-42.
    4. Yin, Xiangxin & Dai, Haifeng & Zhao, Lingzhi & Zhao, Donghua & Xiao, Rui & Sun, Yongzheng, 2024. "Control costs of long-range interacting multi-agent systems with noise perturbation," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).

    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:104:y:2017:i:c:p:813-826. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.