Consiglio Nazionale delle Ricerche

Tipo di prodottoArticolo in rivista
TitoloLinear stability in networks of pulse-coupled neurons
Anno di pubblicazione2014
Autore/iSimona Olmi (1,2); Alessandro Torcini (1,2); Antonio Politi (1,3)
Affiliazioni autori(1) Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, Sesto Fiorentino, Italy (2) INFN--Sezione di Firenze and CSDC, Sesto Fiorentino, Italy (3) SUPA and Institute for Complex Systems and Mathematical Biology, King's College, University of Aberdeen, Aberdeen, UK
Autori CNR e affiliazioni
  • inglese
AbstractIn a first step toward the comprehension of neural activity, one should focus on the stability of the possible dynamical states. Even the characterization of an idealized regime, such as that of a perfectly periodic spiking activity, reveals unexpected difficulties. In this paper we discuss a general approach to linear stability of pulse-coupled neural networks for generic phase-response curves and post-synaptic response functions. In particular, we present: (1) a mean-field approach developed under the hypothesis of an infinite network and small synaptic conductances; (2) a "microscopic" approach which applies to finite but large networks. As a result, we find that there exist two classes of perturbations: those which are perfectly described by the mean-field approach and those which are subject to finite-size corrections, irrespective of the network size. The analysis of perfectly regular, asynchronous, states reveals that their stability depends crucially on the smoothness of both the phase-response curve and the transmitted post-synaptic pulse. Numerical simulations suggest that this scenario extends to systems that are not covered by the perturbative approach. Altogether, we have described a series of tools for the stability analysis of various dynamical regimes of generic pulse-coupled oscillators, going beyond those that are currently invoked in the literature.
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Pagine da-
Pagine aart_n_8
Pagine totali14
RivistaFrontiers in computational neuroscience
Attiva dal 2007
Editore: Frontiers Research Foundation, - Lausanne
Paese di pubblicazione: Svizzera
Lingua: inglese
ISSN: 1662-5188
Titolo chiave: Frontiers in computational neuroscience
Titolo proprio: Frontiers in computational neuroscience
Titolo abbreviato: Front. comput. neurosci.
Numero volume della rivista8
Fascicolo della rivistaFebruary
Verificato da refereeSì: Internazionale
Stato della pubblicazionePublished version
Indicizzazione (in banche dati controllate)
  • Scopus (Codice:2-s2.0-84893618431)
  • ISI Web of Science (WOS) (Codice:000332510000001)
Parole chiavelinear stability analysis, splay states, neural networks, pulse coupled neurons, Floquet spectrum
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Note/Altre informazioniThis article is part of the Research Topic Application of Nonlinear Analysis to the Study of Complex Systems in Neuroscience and Behavioral Research, edited by Tobias A. Mattei.
Strutture CNR
  • ISC — ISC - Sede secondaria di Firenze - Sesto Fiorentino
Moduli/Attività/Sottoprogetti CNR
  • MD.P02.017.001 : comportamento dinamico di sistemi complessi
Progetti Europei
Articolo pubblicato
Descrizione: Open access
Tipo documento: application/x-pdf