Generalized ratecode model for neuron ensembles with finite populations
Abstract
We have proposed a generalized Langevintype ratecode model subjected to multiplicative noise, in order to study stationary and dynamical properties of an ensemble containing a finite number N of neurons. Calculations using the FokkerPlanck equation have shown that, owing to the multiplicative noise, our rate model yields various kinds of stationary nonGaussian distributions such as {gamma}, inverseGaussianlike, and lognormallike distributions, which have been experimentally observed. The dynamical properties of the rate model have been studied with the use of the augmented moment method (AMM), which was previously proposed by the author from a macroscopic point of view for finiteunit stochastic systems. In the AMM, the original Ndimensional stochastic differential equations (DEs) are transformed into threedimensional deterministic DEs for the means and fluctuations of local and global variables. The dynamical responses of the neuron ensemble to pulse and sinusoidal inputs calculated by the AMM are in good agreement with those obtained by direct simulation. The synchronization in the neuronal ensemble is discussed. The variabilities of the firing rate and of the interspike interval are shown to increase with increasing magnitude of multiplicative noise, which may be a conceivable origin of the observed large variability in cortical neurons.
 Authors:
 Department of Physics, Tokyo Gakugei University, Koganei, Tokyo 1848501 (Japan)
 Publication Date:
 OSTI Identifier:
 21072434
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; Journal Volume: 75; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevE.75.051904; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND TECHNOLOGY; BRAIN; COMPUTERIZED SIMULATION; DISTRIBUTION; FLUCTUATIONS; FOKKERPLANCK EQUATION; GAUSS FUNCTION; MOMENTS METHOD; NERVE CELLS; NEURAL NETWORKS; NOISE; STOCHASTIC PROCESSES; SYNCHRONIZATION
Citation Formats
Hasegawa, Hideo. Generalized ratecode model for neuron ensembles with finite populations. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVE.75.051904.
Hasegawa, Hideo. Generalized ratecode model for neuron ensembles with finite populations. United States. doi:10.1103/PHYSREVE.75.051904.
Hasegawa, Hideo. Tue .
"Generalized ratecode model for neuron ensembles with finite populations". United States.
doi:10.1103/PHYSREVE.75.051904.
@article{osti_21072434,
title = {Generalized ratecode model for neuron ensembles with finite populations},
author = {Hasegawa, Hideo},
abstractNote = {We have proposed a generalized Langevintype ratecode model subjected to multiplicative noise, in order to study stationary and dynamical properties of an ensemble containing a finite number N of neurons. Calculations using the FokkerPlanck equation have shown that, owing to the multiplicative noise, our rate model yields various kinds of stationary nonGaussian distributions such as {gamma}, inverseGaussianlike, and lognormallike distributions, which have been experimentally observed. The dynamical properties of the rate model have been studied with the use of the augmented moment method (AMM), which was previously proposed by the author from a macroscopic point of view for finiteunit stochastic systems. In the AMM, the original Ndimensional stochastic differential equations (DEs) are transformed into threedimensional deterministic DEs for the means and fluctuations of local and global variables. The dynamical responses of the neuron ensemble to pulse and sinusoidal inputs calculated by the AMM are in good agreement with those obtained by direct simulation. The synchronization in the neuronal ensemble is discussed. The variabilities of the firing rate and of the interspike interval are shown to increase with increasing magnitude of multiplicative noise, which may be a conceivable origin of the observed large variability in cortical neurons.},
doi = {10.1103/PHYSREVE.75.051904},
journal = {Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics},
number = 5,
volume = 75,
place = {United States},
year = {Tue May 15 00:00:00 EDT 2007},
month = {Tue May 15 00:00:00 EDT 2007}
}

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