Consiglio Nazionale delle Ricerche

Tipo di prodottoArticolo in rivista
TitoloSplay States in Finite Pulse-Coupled Networks of Excitable Neurons
Anno di pubblicazione2012
Formato
  • Elettronico
  • Cartaceo
Autore/iDipoppa, M. (1,2,3); Krupa, M. (1,4); Torcini Alessandro (5,6,7); Gutkin Boris S. (1,2)
Affiliazioni autori1. Ecole Normale Super, Dept Etudes Cognit, Grp Neural Theory, LNC, F-75005 Paris, France 2. INSERM, Lab Neurosci Cognit, U960, F-75005 Paris, France 3. Univ Paris 06, F-75005 Paris, France 4. Radboud Univ Nijmegen, Donders Inst Brain Cognit & Behav, Dept Med Phys & Biophys, NL-6525 EZ Nijmegen, Netherlands 5. Ist Nazl Fis Nucl, Sez Firenze, I-50019 Sesto Fiorentino, Italy 6. CNR, Ist Sistemi Complessi, I-50019 Sesto Fiorentino, Italy 7. Ctr Interdipartimentale Studio Dinam Complesse, I-50019 Sesto Fiorentino, Italy
Autori CNR e affiliazioni
  • ALESSANDRO TORCINI
Lingua/e
  • inglese
AbstractThe emergence and stability of splay states is studied in fully coupled finite networks of N excitable quadratic integrate-and-fire neurons, connected via synapses modeled as pulses of finite amplitude and duration. For such synapses, by introducing two distinct types of synaptic events (pulse emission and termination), we were able to write down an exact event-driven map for the system and to evaluate the splay state solutions. For M overlapping postsynaptic potentials, the linear stability analysis of the splay state should also take in account, besides the actual values of the membrane potentials, the firing times associated with the M previous pulse emissions. As a matter of fact, it was possible, by introducing M complementary variables, to rephrase the evolution of the network as an event-driven map and to derive an analytic expression for the Floquet spectrum. We find that, independently of M, the splay state is marginally stable with N - 2 neutral directions. Furthermore, we have identified a family of periodic solutions surrounding the splay state and sharing the same neutral stability directions. In the limit of delta-pulses, it is still possible to derive an event-driven formulation for the dynamics; however, the number of neutrally stable directions associated with the splay state becomes N. Finally, we prove a link between the results for our system and a previous theory [S. Watanabe and S. H. Strogatz, Phys. D, 74 (1994), pp. 197-253] developed for networks of phase oscillators with sinusoidal coupling.
Lingua abstractinglese
Altro abstract-
Lingua altro abstract-
Pagine da864
Pagine a894
Pagine totali31
RivistaSIAM journal on applied dynamical systems
Attiva dal 2002
Editore: Society of Industrial and Applied Mathematics, - Philadelphia, PA
Paese di pubblicazione: Stati Uniti d'America
Lingua: inglese
ISSN: 1536-0040
Titolo chiave: SIAM journal on applied dynamical systems
Titolo proprio: SIAM journal on applied dynamical systems
Titoli alternativi:
  • SIADS
  • Society of Industrial and Applied Mathematics journal on applied dynamical systems
Numero volume della rivista11
Fascicolo della rivista3
DOI10.1137/110859683
Verificato da refereeSì: Internazionale
Stato della pubblicazionePublished version
Indicizzazione (in banche dati controllate)
  • ISI Web of Science (WOS) (Codice:000309977400004)
  • Scopus (Codice:2-s2.0-84866431919)
Parole chiavesplay state, event-driven map, neural network, excitable neurons, Floquet multipliers
Link (URL, URI)http://epubs.siam.org/doi/abs/10.1137/110859683
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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-
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