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Bulletin of Mathematical Biology

, Volume 70, Issue 6, pp 1608–1633 | Cite as

Synchrony and Asynchrony in a Fully Stochastic Neural Network

  • R. E. Lee DeVille
  • Charles S. Peskin
Original Article

Abstract

We describe and analyze a model for a stochastic pulse-coupled neural network, in which the randomness in the model corresponds to synaptic failure and random external input. We show that the network can exhibit both synchronous and asynchronous behavior, and surprisingly, that there exists a range of parameters for which the network switches spontaneously between synchrony and asynchrony. We analyze the associated mean-field model and show that the switching parameter regime corresponds to a bistability in the mean field, and that the switches themselves correspond to rare events in the stochastic system.

Keywords

Neural network Neuronal network Synchronization Mean-field analysis Stochastic integrate-and-fire Bistability Rare events 

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Copyright information

© Society for Mathematical Biology 2008

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of IllinoisUrbanaUSA
  2. 2.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA

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