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

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 fin...

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Detalles Bibliográficos
Autores principales: Olmi, Simona, Politi, Antonio, Torcini, Alessandro
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer 2012
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3606406/
https://www.ncbi.nlm.nih.gov/pubmed/23174267
http://dx.doi.org/10.1186/2190-8567-2-12
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author Olmi, Simona
Politi, Antonio
Torcini, Alessandro
author_facet Olmi, Simona
Politi, Antonio
Torcini, Alessandro
author_sort Olmi, Simona
collection PubMed
description 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 [Formula: see text] 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.
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spelling pubmed-36064062013-03-25 Stability of the splay state in networks of pulse-coupled neurons Olmi, Simona Politi, Antonio Torcini, Alessandro J Math Neurosci Research 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 [Formula: see text] 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. Springer 2012-11-22 /pmc/articles/PMC3606406/ /pubmed/23174267 http://dx.doi.org/10.1186/2190-8567-2-12 Text en Copyright ©2012 Olmi et al.; licensee Springer http://creativecommons.org/licenses/by/2.0 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.
spellingShingle Research
Olmi, Simona
Politi, Antonio
Torcini, Alessandro
Stability of the splay state in networks of pulse-coupled neurons
title Stability of the splay state in networks of pulse-coupled neurons
title_full Stability of the splay state in networks of pulse-coupled neurons
title_fullStr Stability of the splay state in networks of pulse-coupled neurons
title_full_unstemmed Stability of the splay state in networks of pulse-coupled neurons
title_short Stability of the splay state in networks of pulse-coupled neurons
title_sort stability of the splay state in networks of pulse-coupled neurons
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3606406/
https://www.ncbi.nlm.nih.gov/pubmed/23174267
http://dx.doi.org/10.1186/2190-8567-2-12
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AT politiantonio stabilityofthesplaystateinnetworksofpulsecoupledneurons
AT torcinialessandro stabilityofthesplaystateinnetworksofpulsecoupledneurons

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