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

R. E. Lee DeVille; C. S. Peskin; J. H. Spencer

Mathematical Modelling of Natural Phenomena (2010)

- Volume: 5, Issue: 2, page 26-66
- ISSN: 0973-5348

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topLee DeVille, R. E., Peskin, C. S., and Spencer, J. H.. "Dynamics of Stochastic Neuronal Networks and the Connections to Random Graph Theory." Mathematical Modelling of Natural Phenomena 5.2 (2010): 26-66. <http://eudml.org/doc/197622>.

@article{LeeDeVille2010,

abstract = {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 of the connection strength — as the synapses are made more
reliable, there is a sudden onset of synchronous behavior. A detailed understanding of the
dynamics involves both a characterization of the size of the giant component in a certain
random graph process, and control of the pathwise dynamics of the system by obtaining
exponential bounds for the probabilities of events far from the mean.},

author = {Lee DeVille, R. E., Peskin, C. S., Spencer, J. H.},

journal = {Mathematical Modelling of Natural Phenomena},

keywords = {neural network; neuronal network; synchrony; mean-field analysis; integrate-and-fire; random graphs; limit theorem},

language = {eng},

month = {3},

number = {2},

pages = {26-66},

publisher = {EDP Sciences},

title = {Dynamics of Stochastic Neuronal Networks and the Connections to Random Graph Theory},

url = {http://eudml.org/doc/197622},

volume = {5},

year = {2010},

}

TY - JOUR

AU - Lee DeVille, R. E.

AU - Peskin, C. S.

AU - Spencer, J. H.

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

JO - Mathematical Modelling of Natural Phenomena

DA - 2010/3//

PB - EDP Sciences

VL - 5

IS - 2

SP - 26

EP - 66

AB - 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 of the connection strength — as the synapses are made more
reliable, there is a sudden onset of synchronous behavior. A detailed understanding of the
dynamics involves both a characterization of the size of the giant component in a certain
random graph process, and control of the pathwise dynamics of the system by obtaining
exponential bounds for the probabilities of events far from the mean.

LA - eng

KW - neural network; neuronal network; synchrony; mean-field analysis; integrate-and-fire; random graphs; limit theorem

UR - http://eudml.org/doc/197622

ER -

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