Eur. Phys. J. Plus (2016) 131: 411
https://doi.org/10.1140/epjp/i2016-16411-1

Regular Article

A correspondence between the models of Hodgkin-Huxley and FitzHugh-Nagumo revisited

¹ Department of Theoretical Physics, Kursk State University, Radishcheva st. 33, 305000, Kursk, Russia
² Department of Mathematical Analysis and Applied Mathematics, Kursk State University, Radishcheva st. 33, 305000, Kursk, Russia

^* e-mail: postnicov@gmail.com

Received: 22 August 2016
Accepted: 3 November 2016
Published online: 24 November 2016

Abstract

We present the discussion on the possibility to scale the classical dimensionless FitzHugh-Nagumo model of neuronal self-sustained oscillations to the range of variables corresponding to the results, which are provided by the biophysically relevant reduced two-dimensional Hodgkin-Huxley equations (the Rinzel model). It is shown that there exists a relatively simple choice of affine transformation, which results in time-dependent solutions, which reproduce with a high accuracy the time course of the recovery variable and the sharp onsets (intervals of fast motions on a phase trajectories) of the voltage spikes. As for the latter, the reasons for unavoidable difference are discussed as well as a necessity of taking into account applied current values during such a scaling procedure.