IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v147y2021ics0960077921003283.html
   My bibliography  Save this article

Pattern formation in the Fitzhugh–Nagumo neuron with diffusion relaxation

Author

Listed:
  • Tah, Forwah Amstrong
  • Tabi, Conrad Bertrand
  • Kofane, Timoléon Crépin

Abstract

We examine the spatiotemporal dynamics of the Fitzhugh-nagumo neuron taking into account the effects of relaxation induced by finite speeds of propagation. Stability analysis indicates the presence of Hopf bifurcations induced by relaxation as well as Pitchfork bifurcations due to by diffusion, and independent of the relaxation time. Analysis of the dispersion relation of the oscillatory waves demonstrates that the system, unlike the classical models, allows for finite speeds of propagation for non-negligible values of the relaxation time. Using the center manifold theorem, we reduce the system to its normal form representation both in the strong and weakly coupled limits. From the restricted dynamics, the direction of the Hopf bifurcation is computed, and the collective dynamics inferred. Numerical simulations of the nonlinear wave states of the system show that the uniform oscillatory state is stable against long wave perturbations, indicating full synchronization. The current model might be suitable to describe the dynamics of intracortical neurons, where lack of myelination leads to lower propagation velocities and ultimately larger delays.

Suggested Citation

  • Tah, Forwah Amstrong & Tabi, Conrad Bertrand & Kofane, Timoléon Crépin, 2021. "Pattern formation in the Fitzhugh–Nagumo neuron with diffusion relaxation," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    • Handle: RePEc:eee:chsofr:v:147:y:2021:i:c:s0960077921003283
    DOI: 10.1016/j.chaos.2021.110974
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921003283
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.110974?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. Iqbal, Naveed & Wu, Ranchao & Liu, Biao, 2017. "Pattern formation by super-diffusion in FitzHugh–Nagumo model," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 245-258.
    2. Xu, Ying & Guo, Yeye & Ren, Guodong & Ma, Jun, 2020. "Dynamics and stochastic resonance in a thermosensitive neuron," Applied Mathematics and Computation, Elsevier, vol. 385(C).
    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. Ma, Xiaowen & Xu, Ying, 2022. "Taming the hybrid synapse under energy balance between neurons," Chaos, Solitons & Fractals, Elsevier, vol. 159(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. Mondal, Arnab & Upadhyay, Ranjit Kumar & Mondal, Argha & Sharma, Sanjeev Kumar, 2022. "Emergence of Turing patterns and dynamic visualization in excitable neuron model," Applied Mathematics and Computation, Elsevier, vol. 423(C).
    2. Zheng, Qianqian & Shen, Jianwei, 2020. "Turing instability induced by random network in FitzHugh-Nagumo model," Applied Mathematics and Computation, Elsevier, vol. 381(C).
    3. Mondal, Argha & Hens, Chittaranjan & Mondal, Arnab & Antonopoulos, Chris G., 2021. "Spatiotemporal instabilities and pattern formation in systems of diffusively coupled Izhikevich neurons," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    4. Fateev, I. & Polezhaev, A., 2024. "Chimera states in a lattice of superdiffusively coupled neurons," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    5. Yu, Dong & Wu, Yong & Yang, Lijian & Zhao, Yunjie & Jia, Ya, 2023. "Effect of topology on delay-induced multiple resonances in locally driven systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).
    6. Njitacke, Zeric Tabekoueng & Ramadoss, Janarthanan & Takembo, Clovis Ntahkie & Rajagopal, Karthikeyan & Awrejcewicz, Jan, 2023. "An enhanced FitzHugh–Nagumo neuron circuit, microcontroller-based hardware implementation: Light illumination and magnetic field effects on information patterns," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    7. Feifei Yang & Xikui Hu & Guodong Ren & Jun Ma, 2023. "Synchronization and patterns in a memristive network in noisy electric field," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(6), pages 1-14, June.
    8. Guo, Yeye & Wang, Chunni & Yao, Zhao & Xu, Ying, 2022. "Desynchronization of thermosensitive neurons by using energy pumping," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 602(C).
    9. Ma, Xiaowen & Xu, Ying, 2022. "Taming the hybrid synapse under energy balance between neurons," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    10. Liu, Huixia & Lu, Lulu & Zhu, Yuan & Wei, Zhouchao & Yi, Ming, 2022. "Stochastic resonance: The response to envelope modulation signal for neural networks with different topologies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 607(C).
    11. Kaijun Wu & Jiawei Li, 2023. "Effects of high–low-frequency electromagnetic radiation on vibrational resonance in FitzHugh–Nagumo neuronal systems," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(9), pages 1-19, September.
    12. Zhou, Ping & Yao, Zhao & Ma, Jun & Zhu, Zhigang, 2021. "A piezoelectric sensing neuron and resonance synchronization between auditory neurons under stimulus," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    13. Njitacke, Zeric Tabekoueng & Ramakrishnan, Balamurali & Rajagopal, Karthikeyan & Fonzin Fozin, Théophile & Awrejcewicz, Jan, 2022. "Extremely rich dynamics of coupled heterogeneous neurons through a Josephson junction synapse," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    14. Hussain, Iqtadar & Ghosh, Dibakar & Jafari, Sajad, 2021. "Chimera states in a thermosensitive FitzHugh-Nagumo neuronal network," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    15. Li, Fan & Liu, Shuai & Li, Xiaola, 2022. "Pattern selection in thermosensitive neuron network induced by noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 589(C).
    16. Yao, Zhao & Wang, Chunni, 2022. "Collective behaviors in a multiple functional network with hybrid synapses," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 605(C).
    17. Dai, Shiqi & Lu, Lulu & Wei, Zhouchao & Zhu, Yuan & Yi, Ming, 2022. "Influence of temperature and noise on the propagation of subthreshold signal in feedforward neural network," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    18. Yu, Dong & Lu, Lulu & Wang, Guowei & Yang, Lijian & Jia, Ya, 2021. "Synchronization mode transition induced by bounded noise in multiple time-delays coupled FitzHugh–Nagumo model," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    19. Ding, Qianming & Wu, Yong & Hu, Yipeng & Liu, Chaoyue & Hu, Xueyan & Jia, Ya, 2023. "Tracing the elimination of reentry spiral waves in defibrillation: Temperature effects," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    20. Gao, Chenghua & Qiao, Shuai & An, Xinlei, 2022. "Global multistability and mechanisms of a memristive autapse-based Filippov Hindmash-Rose neuron model," 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:147:y:2021:i:c:s0960077921003283. 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.