Open Access Research

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

Simona Olmi1,2,4, Antonio Politi1,2,3 and Alessandro Torcini1,2,4*

Author Affiliations

1 Istituto dei Sistemi Complessi, CNR - Consiglio Nazionale delle Ricerche, via Madonna del Piano 10, I-50019, Sesto Fiorentino, Italy

2 Centro Interdipartimentale per lo Studio delle Dinamiche Complesse, via Sansone, 1 - I-50019, Sesto Fiorentino, Italy

3 Institute for Complex Systems and Mathematical Biology, King’s College, University of Aberdeen, Aberdeen, AB24 3UE, United Kingdom

4 INFN Sez. Firenze, via Sansone, 1 - I-50019, Sesto Fiorentino, Italy

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The Journal of Mathematical Neuroscience 2012, 2:12 doi:10.1186/2190-8567-2-12

Published: 22 November 2012

Abstract

We analytically investigate the stability of splay states in the networks of N globally pulse-coupled phase-like models of neurons. We develop a perturbative technique which allows determining the Floquet exponents for a generic velocity field and implement the method for a given pulse shape. We find that in the case of discontinuous velocity fields, the Floquet spectrum scales as <a onClick="popup('http://www.mathematical-neuroscience.com/content/2/1/12/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.mathematical-neuroscience.com/content/2/1/12/mathml/M1">View MathML</a> and the stability is determined by the sign of the jump at the discontinuity. Altogether, the form of the spectrum depends on the pulse shape, but it is independent of the velocity field.

PACS: 05.45.Xt, 84.35.+i, 87.19.lj.

Keywords:
pulse-coupled neural networks; Floquet spectra; splay states