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Energy computation and multiplier-less implementation of the two-dimensional FitzHugh–Nagumo (FHN) neural circuit

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Abstract

In this work, with the aim of reducing the cost of the implementation of the traditional 2D FHN neuron circuit, a pair of diodes connected in an anti-parallel direction is used to replace the usual cubic nonlinearity (implemented with two multipliers). Based on the stability of the model, the generation of self-excited firing patterns is justified. Making use of the famous Helmholtz theorem, a Hamilton function is provided for the estimation of the energy released during each electrical activity of the model. From the investigation of the 1D evolution of the maxima of the membrane potential of the model, it was recorded that the considered model is able to experience a period of doubling bifurcation followed by a crisis that enables the increasing of the volume of the attractor. This contribution ends with the realization of a neural circuit without analog multipliers for the validation of the obtained results.

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Data availability

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 funded by the Center for Nonlinear Systems, Chennai Institute of Technology, India, vide funding number CIT/CNS/2023/RP/010. 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. Department of Electrical and Electronic Engineering, College of Technology (COT), University of Buea, P.O. Box 63, Buea, Cameroon

    Zeric Tabekoueng Njitacke

  2. Centre for Nonlinear Systems, Chennai Institute of Technology, Chennai, India

    Gokul Sriram & Karthikeyan Rajagopal

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

    Anitha Karthikeyan

  4. 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. Zeric Tabekoueng Njitacke
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  2. Gokul Sriram
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  3. Karthikeyan Rajagopal
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  4. Anitha Karthikeyan
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  5. Jan Awrejcewicz
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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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Tabekoueng Njitacke, Z., Sriram, G., Rajagopal, K. et al. Energy computation and multiplier-less implementation of the two-dimensional FitzHugh–Nagumo (FHN) neural circuit. Eur. Phys. J. E 46, 60 (2023). https://doi.org/10.1140/epje/s10189-023-00319-1

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