Self-sustained activity in a small-world network of excitable neurons

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Abstract

We study the dynamics of excitable integrate-and-fire neurons in a small-world network. At low densities p of directed random connections, a localized transient stimulus results either in self-sustained persistent activity or in a brief transient followed by failure. Averages over the quenched ensemble reveal that the probability of failure changes from 0 to 1 over a narrow range in p; this failure transition can be described analytically through an extension of an existing mean-field result. Exceedingly long transients emerge at higher densities p; their activity patterns are disordered, in contrast to the mostly periodic persistent patterns observed at low p. The times at which such patterns die out follow a stretched-exponential distribution, which depends sensitively on the propagation velocity of the excitation.

Original languageEnglish (US)
Number of pages1
JournalPhysical review letters
Volume92
Issue number19
DOIs
StatePublished - May 14 2004

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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