Traveling pulses in Class-I excitable media

Arinyo-i-Prats, Andreu; Moreno-Spiegelberg, Pablo; Matı́as, Manuel A.; Gomila, Damià
Submitted (2021)

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 scenar-
ios: 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

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