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

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

2012-01-31

arxiv.org/abs/1201.6594v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

22 pages, no figures and 120 equations

Scientific paper

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.

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