We analytically investigate the stability of 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/N2 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.
- linear stability collective dynamics
Olmi, S., Politi, A., & Torcini, A. (2012). Stability of the splay state in networks of pulse-coupled neurons. The Journal of Mathematical Neuroscience, 2, . https://doi.org/10.1186/2190-8567-2-12