Abstract
We study the dynamics of excitable integrate-and-fire neurons in a small-world network. At low densities 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 to over a narrow range in ; this failure transition can be described analytically through an extension of an existing mean-field result. Exceedingly long transients emerge at higher densities ; their activity patterns are disordered, in contrast to the mostly periodic persistent patterns observed at low . The times at which such patterns die out follow a stretched-exponential distribution, which depends sensitively on the propagation velocity of the excitation.
- Received 9 June 2003
DOI:https://doi.org/10.1103/PhysRevLett.92.198101
©2004 American Physical Society