Investigation of an improved FitzHugh-Rinzel neuron and its multiplier-less circuit implementation

Zeric Njitacke Tabekoueng; Balakrishnan Sriram; Karthikeyan Rajagopal; Anitha Karthikeyan; Jan Awrejcewicz

doi:10.1063/5.0152811

Investigation of an improved FitzHugh-Rinzel neuron and its multiplier-less circuit implementation

Chaos. 2023 Jun 1;33(6):063153. doi: 10.1063/5.0152811.

Authors

Zeric Njitacke Tabekoueng¹, Balakrishnan Sriram², Karthikeyan Rajagopal², Anitha Karthikeyan³, Jan Awrejcewicz⁴

Affiliations

¹ Department of Electrical and Electronic Engineering, College of Technology (COT), University of Buea, P.O. Box 63, Buea, Cameroon.
² Centre for Nonlinear Systems, Chennai Institute of Technology, Chennai 600069, India.
³ Electronics and Communication Engineering, Vemu Institute of Technology, Chittoor 517112, India.
⁴ Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, ul. Stefanowskiego 1/15, Lodz 90-537, Poland.

PMID: 37368042
DOI: 10.1063/5.0152811

Abstract

Circuit implementation of the mathematical model of neurons represents an alternative approach for the validation of their dynamical behaviors for their potential applications in neuromorphic engineering. In this work, an improved FitzHugh-Rinzel neuron, in which the traditional cubic nonlinearity is swapped with a sine hyperbolic function, is introduced. This model has the advantage that it is multiplier-less since the nonlinear component is just implemented with two diodes in anti-parallel. The stability of the proposed model revealed that it has both stable and unstable nodes around its fixed points. Based on the Helmholtz theorem, a Hamilton function that enables the estimation of the energy released during the various modes of electrical activity is derived. Furthermore, numerical computation of the dynamic behavior of the model revealed that it was able to experience coherent and incoherent states involving both bursting and spiking. In addition, the simultaneous appearance of two different types of electric activity for the same neuron parameters is also recorded by just varying the initial states of the proposed model. Finally, the obtained results are validated using the designed electronic neural circuit, which has been analyzed in the Pspice simulation environment.