IDEAS home Printed from https://ideas.repec.org/a/wsi/fracta/v30y2022i10ns0218348x22402630.html
   My bibliography  Save this article

A Fractional Difference Equation Model Of A Simple Neuron Map

Author

Listed:
  • SALEM ALKHALAF

    (Department of Computer Science, College of Science and Arts at ArRass, Qassim University, Buraydah, Saudi Arabia)

  • SURESH KUMARASAMY

    (Centre for Nonlinear Systems, Chennai Institute of Technology, Chennai 600069, India)

  • SUNDARAM ARUN

    (Electronics and Communication Engineering, Jerusulaem College of Engineering, Chennai, Tamilnadu, India)

  • ANITHA KARTHIKEYAN

    (Department of Electronics and Communications Engineering and University, Centre of Research & Development, Chandigarh University, Mohali 140413, Punjab, India)

  • SALAH BOULAARAS

    (Department of Mathematics, College of Sciences, Qassim University, Saudi Arabia)

Abstract

In this work, we present the dynamics of the one dimension fractional-order Rulkov map of biological neurons. The one-dimensional neuron map shows all the dynamical behaviors observed in the real-time experiment. The integer order one-dimensional Rulkov map exhibits chaotic dynamics in the presence of time-dependent external stimuli like periodic sinusoidal force or random Gaussian process. When we construct a large complex network of neurons, the higher system dimension, as well as the external forcing, is always an obstacle. Interestingly, our study shows even with constant external stimuli, the fractional-order one-dimensional neuron shows a rich variety of complex dynamics including chaotic dynamics. We present our results based on the Lyapunov exponent of the fractional-order systems.

Suggested Citation

  • Salem Alkhalaf & Suresh Kumarasamy & Sundaram Arun & Anitha Karthikeyan & Salah Boulaaras, 2022. "A Fractional Difference Equation Model Of A Simple Neuron Map," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(10), pages 1-7, December.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:10:n:s0218348x22402630
    DOI: 10.1142/S0218348X22402630
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0218348X22402630
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0218348X22402630?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.

    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:wsi:fracta:v:30:y:2022:i:10:n:s0218348x22402630. 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: Tai Tone Lim (email available below). General contact details of provider: https://www.worldscientific.com/worldscinet/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.