IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v156y2022ics0960077922000352.html
   My bibliography  Save this article

Codimension two bifurcation in a coupled FitzHugh–Nagumo system with multiple delays

Author

Listed:
  • Achouri, Houssem
  • Aouiti, Chaouki
  • Hamed, Bassem Ben

Abstract

In this paper, a coupled FitzHugh–Nagumo system with multiple delays is considered. In a first step, the critical point at which a zero root of multiplicity two occurs in the characteristic equation is constructed. In a second step, in order to ensure that all the roots of the characteristic equation except for the double zero root have negative real parts, the zeros of a third and a fourth degree exponential polynomial are studied. Moreover, the critical values where the Bogdanov–Takens bifurcation occurs are derived. By using the normal form theory and reduction on the centre manifold, the truncated normal form is obtained, and throughout the bifurcation diagram, its dynamical behaviours are studied. Finally, a numerical example is given to demonstrate our results.

Suggested Citation

  • Achouri, Houssem & Aouiti, Chaouki & Hamed, Bassem Ben, 2022. "Codimension two bifurcation in a coupled FitzHugh–Nagumo system with multiple delays," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    • Handle: RePEc:eee:chsofr:v:156:y:2022:i:c:s0960077922000352
    DOI: 10.1016/j.chaos.2022.111824
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077922000352
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2022.111824?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. Chaouki Aouiti & El abed Assali & Jinde Cao & Ahmed Alsaedi, 2018. "Global exponential convergence of neutral-type competitive neural networks with multi-proportional delays, distributed delays and time-varying delay in leakage delays," International Journal of Systems Science, Taylor & Francis Journals, vol. 49(10), pages 2202-2214, July.
    2. Shengwei Yao & Huonian Tu, 2014. "Stability Switches and Hopf Bifurcation in a Coupled FitzHugh-Nagumo Neural System with Multiple Delays," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-13, July.
    3. Anderson Hoff & Juliana Santos & Cesar Manchein & Holokx Albuquerque, 2014. "Numerical bifurcation analysis of two coupled FitzHugh-Nagumo oscillators," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 87(7), pages 1-9, July.
    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. Chen, Jing & Xiao, Min & Wu, Xiaoqun & Wang, Zhengxin & Cao, Jinde, 2022. "Spatiotemporal dynamics on a class of (n+1)-dimensional reaction–diffusion neural networks with discrete delays and a conical structure," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    2. Chesebro, Anthony G. & Mujica-Parodi, Lilianne R. & Weistuch, Corey, 2023. "Ion gradient-driven bifurcations of a multi-scale neuronal model," Chaos, Solitons & Fractals, Elsevier, vol. 167(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. N. C. Pati, 2023. "Bifurcations and multistability in a physically extended Lorenz system for rotating convection," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(8), pages 1-15, August.
    2. Wang, Zhizhi & Hu, Bing & Zhou, Weiting & Xu, Minbo & Wang, Dingjiang, 2023. "Hopf bifurcation mechanism analysis in an improved cortex-basal ganglia network with distributed delays: An application to Parkinson’s disease," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    3. Wang, Guowei & Yu, Dong & Ding, Qianming & Li, Tianyu & Jia, Ya, 2021. "Effects of electric field on multiple vibrational resonances in Hindmarsh-Rose neuronal systems," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    4. Rao, Xiao-Bo & Zhao, Xu-Ping & Chu, Yan-Dong & Zhang, Jian-Gang & Gao, Jian-She, 2020. "The analysis of mode-locking topology in an SIR epidemic dynamics model with impulsive vaccination control: Infinite cascade of Stern-Brocot sum trees," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    5. Xiaohui Xu & Jibin Yang & Yanhai Xu, 2019. "Mean Square Exponential Stability of Stochastic Complex-Valued Neural Networks with Mixed Delays," Complexity, Hindawi, vol. 2019, pages 1-20, June.
    6. Das, Saureesh, 2022. "Recurrence quantification and bifurcation analysis of electrical activity in resistive/memristive synapse coupled Fitzhugh–Nagumo type neurons," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    7. Karthick, S.A. & Sakthivel, R. & Ma, Y.K. & Leelamani, A., 2020. "Observer based guaranteed cost control for Markovian jump stochastic neutral-type neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    8. Egorov, Nikita M. & Sysoev, Ilya V. & Ponomarenko, Vladimir I. & Sysoeva, Marina V., 2022. "Complex regimes in electronic neuron-like oscillators with sigmoid coupling," Chaos, Solitons & Fractals, Elsevier, vol. 160(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:156:y:2022:i:c:s0960077922000352. 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.