PMID: 12786392Jun 6, 2003Paper

Dynamical mean-field theory of spiking neuron ensembles: response to a single spike with independent noises

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Hideo Hasegawa

Abstract

A semianalytical dynamical mean-field theory has been developed for a study of dynamics of an ensemble of N-unit FitzHugh-Nagumo neurons subject to white noises. Assuming weak noises and the Gaussian distribution of state variables, we have driven equations of motions for moments of local and global variables. Dynamical mean-field approximation (DMA) has replaced original, 2N-dimensional stochastic differential equations (DEs) by eight-dimensional deterministic DEs, whereas the conventional moment method yields N(2N+3)-dimensional deterministic DEs for local variables. We have discussed the dependence of the spike firing precision and the synchronization on the noise intensity, synaptic coupling, and the size of the neuron ensemble. The spike timing precision is shown to be improved by increasing the size of the neuron ensemble, even when there are no couplings among neurons. When the coupling is introduced, neurons in ensembles respond to an input spike with a partial synchronization. Results calculated by our DMA theory are in good agreement with those obtained by direct simulations. DMA theory is extended to a large cluster which can be divided into multiple subclusters according to their functions. A model calculation has d...Continue Reading

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Citations

Nov 7, 2008·Journal of Computational Neuroscience·Chin-Yueh Liu, Duane Q Nykamp
Jul 24, 2013·Proceedings of the National Academy of Sciences of the United States of America·Adrián Ponce-AlvarezGustavo Deco
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Nov 18, 2008·NeuroImage·André C MarreirosKarl J Friston
Dec 20, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Hideo Hasegawa
Sep 28, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Hideo Hasegawa
Sep 28, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Hideo Hasegawa
Feb 9, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Hideo Hasegawa
Feb 21, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Lucas S Furtado, Mauro Copelli
Apr 12, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Leonid A Safonov, Yoshiharu Yamamoto
May 23, 2006·Physical Review Letters·Aaditya V Rangan, David Cai
Oct 10, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Brent DoironAlex Reyes
Aug 7, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Hideo Hasegawa
Jun 4, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Hideo Hasegawa
Oct 15, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Hideo Hasegawa
Jan 15, 2016·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Vladimir Klinshov, Igor Franović
Jan 20, 2018·Physical Review. E·Igor FranovićVladimir I Nekorkin
Dec 31, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Hideo Hasegawa
Feb 16, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Igor FranovićNikola Burić

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