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Phys Rev Lett. 2004 May 14;92(19):198101. Epub 2004 May 11.

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

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Engineering Science and Applied Mathematics, Northwestern University, Evanston, Illinois 60208, USA.


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.

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