Linear stability in networks of pulse-coupled neurons (Articolo in rivista)

Type
Label
  • Linear stability in networks of pulse-coupled neurons (Articolo in rivista) (literal)
Anno
  • 2014-01-01T00:00:00+01:00 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#doi
  • 10.3389/fncom.2014.00008 (literal)
Alternative label
  • Simona Olmi (1,2); Alessandro Torcini (1,2); Antonio Politi (1,3) (2014)
    Linear stability in networks of pulse-coupled neurons
    in Frontiers in computational neuroscience
    (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
  • Simona Olmi (1,2); Alessandro Torcini (1,2); Antonio Politi (1,3) (literal)
Pagina fine
  • art_n_8 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#altreInformazioni
  • This 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. (literal)
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  • http://journal.frontiersin.org/Journal/10.3389/fncom.2014.00008/abstract (literal)
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  • 8 (literal)
Rivista
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  • 14 (literal)
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  • February (literal)
Note
  • Scopu (literal)
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  • (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 (literal)
Titolo
  • Linear stability in networks of pulse-coupled neurons (literal)
Abstract
  • In 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. (literal)
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