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

@article{Roxin2004SelfsustainedAI,
  title={Self-sustained activity in a small-world network of excitable neurons.},
  author={Alex Roxin and Hermann Riecke and Sara A. Solla},
  journal={Physical review letters},
  year={2004},
  volume={92 19},
  pages={
          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 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… Expand

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