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

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

2003-09-25

arxiv.org/abs/nlin/0309067v1

Nonlinear Sciences

Pattern Formation and Solitons

4 pages 6 figures

Scientific paper

10.1103/PhysRevLett.92.198101

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 in either 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 are consistent with a stretched-exponential distribution, which depends sensitively on the propagation velocity of the excitation.

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