Self-Sustained Activity in a Small-World Network of Excitable Neurons

Alex Roxin, Hermann Riecke, and Sara A. Solla
Phys. Rev. Lett. 92, 198101 – Published 11 May 2004

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.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Received 9 June 2003

DOI:https://doi.org/10.1103/PhysRevLett.92.198101

©2004 American Physical Society

Authors & Affiliations

Alex Roxin1,*, Hermann Riecke1, and Sara A. Solla2

  • 1Engineering Science and Applied Mathematics, Northwestern University, Evanston, Illinois 60208, USA
  • 2Department of Physiology and Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, USA

  • *Present address: Neurophysics and Physiology of the Motor System, Université René Descartes, Paris, France.

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 92, Iss. 19 — 14 May 2004

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review Letters

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×