Pulse propagation in discrete systems of coupled excitable cells

TL;DR

This paper analyzes pulse propagation in discrete FitzHugh-Nagumo systems modeling myelinated fibers, providing asymptotic solutions, conditions for propagation failure, and formulas for pulse speed and length.

Contribution

It introduces an asymptotic construction of pulses in discrete FitzHugh-Nagumo systems, aligning well with simulations and exploring pulse initiation and boundary effects.

Findings

Pulse speed and length formulas derived

Propagation failure conditions identified

Asymptotic solutions match numerical simulations

Abstract

Propagation of pulses in myelinated fibers may be described by appropriate solutions of spatially discrete FitzHugh-Nagumo systems. In these systems, propagation failure may occur if either the coupling between nodes is not strong enough or the recovery is too fast. We give an asymptotic construction of pulses for spatially discrete FitzHugh-Nagumo systems which agrees well with numerical simulations and discuss evolution of initial data into pulses and pulse generation at a boundary. Formulas for the speed and length of pulses are also obtained.