IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v118y2019icp311-319.html
   My bibliography  Save this article

Generalized synchronization of the extended Hindmarsh–Rose neuronal model with fractional order derivative

Author

Listed:
  • Giresse, Tene Alain
  • Crepin, Kofane Timoleon
  • Martin, Tchoffo

Abstract

In the present paper, the synchronization of the extended Hindmarsh–Rose neuronal model with fractional order derivative is presented in detail taking into consideration the effects of the very slow intracellular exchange of calcium ion (Ca2+) occurring between cytoplasm and its store. That is, we approach the synchronization by the Ge–Yao–Chen partial region stability theory. The method of resolution used is the powerful Adam–Bashforth–Moulton method which converges quickly to the exact solution. Numerical simulations of the error dynamics proved the effectiveness of the control method. The synchronization time is evaluated for different orders of the derivative and its analysis shows that, it is closely related to the order of the derivative and that fractional order induces quick synchronization compared to integer order.

Suggested Citation

  • Giresse, Tene Alain & Crepin, Kofane Timoleon & Martin, Tchoffo, 2019. "Generalized synchronization of the extended Hindmarsh–Rose neuronal model with fractional order derivative," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 311-319.
    • Handle: RePEc:eee:chsofr:v:118:y:2019:i:c:p:311-319
    DOI: 10.1016/j.chaos.2018.11.028
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S096007791830451X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2018.11.028?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. Shichang Ma & Yufeng Xu & Wei Yue, 2012. "Numerical Solutions of a Variable-Order Fractional Financial System," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-14, September.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Liu, Dan & Zhao, Song & Luo, Xiaoyuan & Yuan, Yi, 2021. "Synchronization for fractional-order extended Hindmarsh-Rose neuronal models with magneto-acoustical stimulation input," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    2. Fateev, I. & Polezhaev, A., 2024. "Chimera states in a lattice of superdiffusively coupled neurons," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).

    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. Zúñiga-Aguilar, C.J. & Gómez-Aguilar, J.F. & Escobar-Jiménez, R.F. & Romero-Ugalde, H.M., 2019. "A novel method to solve variable-order fractional delay differential equations based in lagrange interpolations," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 266-282.
    2. Souad Bensid Ahmed & Adel Ouannas & Mohammed Al Horani & Giuseppe Grassi, 2022. "The Discrete Fractional Variable-Order Tinkerbell Map: Chaos, 0–1 Test, and Entropy," Mathematics, MDPI, vol. 10(17), pages 1-13, September.
    3. Vasily E. Tarasov, 2019. "On History of Mathematical Economics: Application of Fractional Calculus," Mathematics, MDPI, vol. 7(6), pages 1-28, June.

    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:118:y:2019:i:c:p:311-319. 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.