Stability of the splay state in networks of pulse-coupled neurons

TL;DR

This paper analytically studies the stability of splay states in large networks of pulse-coupled neurons, revealing how the Floquet spectrum scales with network size and depends on pulse shape and discontinuities.

Contribution

It introduces a perturbative method to analyze splay state stability and shows the spectrum's dependence on pulse shape and discontinuities, independent of velocity fields.

Findings

Floquet spectrum scales as 1/N^2 for large N

Stability depends on the sign of the jump at discontinuity

Spectrum form depends on pulse shape, not velocity field

Abstract

We analytically investigate the stability of {\it splay states} in networks of $N$ pulse-coupled phase-like models of neurons. By developing a perturbative technique, we find that, in the limit of large $N$, the Floquet spectrum scales as $1/N^2$ for generic discontinuous velocity fields. Moreover, the stability of the so-called short-wavelength component is determined by the sign of the jump at the discontinuity. Altogether, the form of the spectrum depends on the pulse shape but is independent of the velocity field.