Analog simulation of neural information propagation using an electrical FitzHugh–Nagumo lattice P. Marqui  e a, * , J.C. Comte b , S. Morfu c a Laboratoire LE2I, FRE CNRS 2309, Universit e de Bourgogne, BP 47870-21078 Dijon Cedex, France b Department of Physics, University of Crete and Foundation for Research and Technology-Hellas, P.O. Box 2208, 71003 Heraklion, Crete, Greece c Laboratoire dÕAstrophysique, CNRS UMR 6525, Universit e de Nice Sophia-Antipolis, Parc Valrose, 06108 Nice Cedex 2, France Accepted 16 April 2003 Abstract A nonlinear electrical lattice modelling neural information propagation is presented. It is shown that our system is an analog simulator of the FitzHugh–Nagumo equations, and hence supports pulse propagation with the appropriate properties. Ó 2003 Elsevier Ltd. All rights reserved. 1. Introduction As reaction–diffusion equations arise in many areas of physics, biology, chemistry or ecology (see e.g. [1]), a growing interest has been devoted in recent years, to nonlinear information processes in reaction–diffusion systems. Among them, and to just focus on this example, is the neural system. Indeed, the knowledge of the neural information propagation mechanisms constitutes one of most exciting scientific challenge, both from a medical point of view and for the potential bio-inspired applications in transmission and signal processing. Mathematically, the description of the neural action potential propagation obeys to the well-known FitzHugh–Nagumo (F–N) system of two coupled equations [1,2]. This system allowing pulse propagation can be reduced to the single Nagumo equation which permits then front or kink propagation. Experimentally, since the pioneering work of Nagumo [3] who presented an electrical lattice modelling the above-cited Nagumo equation, most of the studies devoted to reaction–diffusion systems have also focused on this equation (see e.g. [4] and references therein). Then, only front propagation properties were considered. The main purpose of this letter is to present an electrical diffusive lattice simulating the whole F–N system, allowing then the study of pulse propagation properties. First, we describe the electrical structure of the lattice and derive the related system of equations. Then, several properties of pulse propagation are verified (profile, velocity), by means of both electrical PSpice simulations and numerical simulations, proving that our electrical lattice is an analog simulator of the F–N system. 2. Description of the electrical lattice We consider a nonlinear electrical lattice realized with N elementary cells, resistively coupled by linear resistors R,as represented in Fig. 1. Each cell contains a linear capacitor in parallel with both a linear self-inductance L and a nonlinear resistor R NL , whose current–voltage characteristic obeys the following cubic law: * Corresponding author. E-mail address: marquie@u-bourgogne.fr (P. Marqui  e). 0960-0779/04/$ - see front matter Ó 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0960-0779(03)00190-5 Chaos, Solitons and Fractals 19 (2004) 27–30 www.elsevier.com/locate/chaos