Traveling pulses in Class-I excitable media

TL;DR

This paper investigates traveling pulses in one-dimensional Class-I excitable media, revealing how bifurcation types influence pulse shape and scaling behaviors, with implications for understanding excitability in various systems.

Contribution

It introduces a general model for Class-I excitability showing how bifurcation types affect traveling pulse properties and scaling behaviors.

Findings

Pulse shape inherits bifurcation-induced infinite period scaling.

Scaling behaviors in spatial pulse thickness mirror temporal characteristic times.

Distinct properties of Class-I excitability lead to unique pulse dynamics.

Abstract

We study Class-I excitable $1$-dimensional media showing the appearance of propagating traveling pulses. We consider a general model exhibiting Class-I excitability mediated by two different scenarios: a homoclinic (saddle-loop) and a SNIC (Saddle-Node on the Invariant Circle) bifurcations. The distinct properties of Class-I with respect to Class-II excitability infer unique properties to traveling pulses in Class-I excitable media. We show how the pulse shape inherit the infinite period of the homoclinic and SNIC bifurcations at threshold, exhibiting scaling behaviors in the spatial thickness of the pulses that are equivalent to the scaling behaviors of characteristic times in the temporal case.