Self-sustained activity in a small-world network of excitable neurons.
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.
Roxin
Alex
A
Engineering Science and Applied Mathematics, Northwestern University, Evanston, Illinois 60208, USA.
Riecke
Hermann
H
Solla
Sara A
SA
D000200:Action Potentials / Q000502:physiology; D009415:Nerve Net / Q000502:physiology*; D016571:Neural Networks, Computer; D009474:Neurons / Q000502:physiology*