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Effect of external excitation on the isolated and collective dynamics of a generic FitzHugh–Rinzel neuron

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Abstract

This contribution considers the isolated and collective dynamics of a FitzHugh–Rinzel (FHR) neuron obtained by adding a third variable to the generic FitzHugh–Nagumo neural circuit. From the Kirchhoff electrical circuit laws, the state equations of the model are derived; afterward, the stability around a zero time constant is investigated, and the hidden dynamics of the model is revealed. Analytical and theoretical investigation of the energy is done to support the various firing activities, such as bursting and spiking, captured in the model. Using the well-known modulation instability theory, the collective behavior of a network made of 50 neurons is analyzed in a chain configuration. As a result, regular patterns consisting of alternate bright and dark bands that are almost periodic and localized in space and time are found. Also, the brighter regions correspond to the regions where the neurons fire, while in the dark regions, the neurons are quiescent. Finally, the brighter regions could be pictured as individual spikes within a burst.

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Data Availability Statement

This manuscript has associated data in a data repository. [Authors’ comment: The data used to support the findings of this study are available from the corresponding author upon request.]

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Acknowledgements

This work is partially funded by Centre for Nonlinear Systems, Chennai Institute of Technology, India, vide Funding Number CIT/CNS/2023/RP/005. Jan Awrejcewicz has been supported by the Polish National Science Centre under the Grant OPUS 18No.2019/35/B/ST8/00980.

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Authors and Affiliations

  1. Centre for Artificial Intelligence, Chennai Institute of Technology, Chennai, India

    Janarthanan Ramadoss

  2. Department of Electrical and Electronic Engineering, College of Technology (COT), University of Buea, P.O.Box 63, Buea, Cameroon

    Clovis Ntahkie Takembo & Zeric Tabekoueng Njitacke

  3. Department of Electronics and Communication Engineering, Vemu Institute of Technology, Chithoor, India

    Anitha Karthikeyan

  4. Department of Electronics and Communications Engineering and University Centre for Research & Development, Chandigarh University, Mohali, 140413, Punjab, India

    Anitha Karthikeyan

  5. Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, ul. Stefanowskiego 1/15, 90-537, Lodz, Poland

    Jan Awrejcewicz

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  1. Janarthanan Ramadoss
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  2. Clovis Ntahkie Takembo
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  3. Anitha Karthikeyan
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  4. Zeric Tabekoueng Njitacke
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All the authors have contributed equally to this manuscript.

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Correspondence to Zeric Tabekoueng Njitacke.

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Ramadoss, J., Takembo, C.N., Karthikeyan, A. et al. Effect of external excitation on the isolated and collective dynamics of a generic FitzHugh–Rinzel neuron. Eur. Phys. J. Plus 138, 962 (2023). https://doi.org/10.1140/epjp/s13360-023-04620-y

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