https://doi.org/10.1140/epjp/s13360-023-04620-y
Regular Article
Effect of external excitation on the isolated and collective dynamics of a generic FitzHugh–Rinzel neuron
1
Centre for Artificial Intelligence, Chennai Institute of Technology, Chennai, India
2
Department of Electrical and Electronic Engineering, College of Technology (COT), University of Buea, P.O.Box 63, Buea, Cameroon
3
Department of Electronics and Communication Engineering, Vemu Institute of Technology, Chithoor, India
4
Department of Electronics and Communications Engineering and University Centre for Research & Development, Chandigarh University, 140413, Mohali, Punjab, India
5
Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, ul. Stefanowskiego 1/15, 90-537, Lodz, Poland
Received:
15
August
2023
Accepted:
23
October
2023
Published online:
30
October
2023
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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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
