Stability of the splay state in networks of pulse-coupled neurons    [PDF]

Simona Olmi, Antonio Politi, Alessandro Torcini
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.
View original: http://arxiv.org/abs/1201.6594