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Dynamics of Stochastic Neuronal Networks and the Connections to Random Graph Theory

R. E. Lee DeVilleC. S. PeskinJ. H. Spencer — 2010

Mathematical Modelling of Natural Phenomena

We analyze a stochastic neuronal network model which corresponds to an all-to-all network of discretized integrate-and-fire neurons where the synapses are failure-prone. This network exhibits different phases of behavior corresponding to synchrony and asynchrony, and we show that this is due to the limiting mean-field system possessing multiple attractors. We also show that this mean-field limit exhibits a first-order phase transition as a function...

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