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

• Published in: The European physical journal. E, Soft matter and biological physics Vol. 46; no. 7; p. 60
• Main Authors: Tabekoueng Njitacke, Zeric, Sriram, Gokul, Rajagopal, Karthikeyan, Karthikeyan, Anitha, Awrejcewicz, Jan
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2023; Springer Nature B.V
• Subjects: Analog circuits; Biological and Medical Physics; Biophysics; Complex Fluids and Microfluidics; Complex Systems; Condensed matter physics; Multipliers; Nanotechnology; Physics; Physics and Astronomy; Polymer Sciences; Regular Article - Flowing Matter; Soft and Granular Matter; Surfaces and Interfaces; Thin Films
• ISSN: 1292-8941; 1292-895X; 1292-895X
• DOI: 10.1140/epje/s10189-023-00319-1

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. Graphical Abstract