IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i8p1312-d395822.html
   My bibliography  Save this article

Entrainment of Weakly Coupled Canonical Oscillators with Applications in Gradient Frequency Neural Networks Using Approximating Analytical Methods

Author

Listed:
  • AmirAli Farokhniaee

    (Department of Physics, University of Connecticut, Storrs, CT 06269, USA
    Music Dynamics Laboratory, Department of Psychology, University of Connecticut, Storrs, CT 06269, USA
    Current address: School of Electrical & Electronic Engineering, University College Dublin, Dublin, Ireland.)

  • Felix V. Almonte

    (Center for Complex Systems and Brain Sciences, Florida Atlantic University, Boca Raton, FL 33431, USA)

  • Susanne Yelin

    (Department of Physics, University of Connecticut, Storrs, CT 06269, USA
    Department of Physics, Harvard University, Cambridge, MA 02138, USA)

  • Edward W. Large

    (Music Dynamics Laboratory, Department of Psychology, University of Connecticut, Storrs, CT 06269, USA)

Abstract

Solving phase equations for systems with high degrees of nonlinearities is cumbersome. However, in the case of two coupled canonical oscillators, that is, a reduced model of translated Wilson–Cowan neuronal dynamics, under slowly varying amplitude and rotating wave approximations, we suggested a convenient way to find their average relative phase evolution. This approach enabled us to find an explicit solution for the average relative phase of the two coupled canonical oscillators based on the original neuronal model parameters, and importantly, to find their phase-locking constraint. This methodology is straightforward to implement in any Wilson–Cowan-type coupled oscillators with applications in gradient frequency neural networks (GFNNs).

Suggested Citation

  • AmirAli Farokhniaee & Felix V. Almonte & Susanne Yelin & Edward W. Large, 2020. "Entrainment of Weakly Coupled Canonical Oscillators with Applications in Gradient Frequency Neural Networks Using Approximating Analytical Methods," Mathematics, MDPI, vol. 8(8), pages 1-20, August.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:8:p:1312-:d:395822
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/8/1312/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/8/1312/
    Download Restriction: no
    ---><---

    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:gam:jmathe:v:8:y:2020:i:8:p:1312-:d:395822. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.