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

Simona Olmi; Antonio Politi; Alessandro Torcini

doi:10.1186/2190-8567-2-12

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

Simona Olmi, Antonio Politi, Alessandro Torcini

CNR, ISC

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Abstract

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.

Original language	English
Article number	12
Number of pages	28
Journal	The Journal of Mathematical Neuroscience
Volume	2
DOIs	https://doi.org/10.1186/2190-8567-2-12
Publication status	Published - 22 Nov 2012

Keywords

linear stability collective dynamics

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10.1186/2190-8567-2-12

art%3A10.1186%2F2190-8567-2-12
© 2012 Olmi et al.; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Stability of the splay state in networks of pulse-coupled neurons

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