Stochastic synchronization of neuronal populations with intrinsic and extrinsic noise.

Handle URI:
http://hdl.handle.net/10754/596818
Title:
Stochastic synchronization of neuronal populations with intrinsic and extrinsic noise.
Authors:
Bressloff, Paul C; Lai, Yi Ming
Abstract:
We extend the theory of noise-induced phase synchronization to the case of a neural master equation describing the stochastic dynamics of an ensemble of uncoupled neuronal population oscillators with intrinsic and extrinsic noise. The master equation formulation of stochastic neurodynamics represents the state of each population by the number of currently active neurons, and the state transitions are chosen so that deterministic Wilson-Cowan rate equations are recovered in the mean-field limit. We apply phase reduction and averaging methods to a corresponding Langevin approximation of the master equation in order to determine how intrinsic noise disrupts synchronization of the population oscillators driven by a common extrinsic noise source. We illustrate our analysis by considering one of the simplest networks known to generate limit cycle oscillations at the population level, namely, a pair of mutually coupled excitatory (E) and inhibitory (I) subpopulations. We show how the combination of intrinsic independent noise and extrinsic common noise can lead to clustering of the population oscillators due to the multiplicative nature of both noise sources under the Langevin approximation. Finally, we show how a similar analysis can be carried out for another simple population model that exhibits limit cycle oscillations in the deterministic limit, namely, a recurrent excitatory network with synaptic depression; inclusion of synaptic depression into the neural master equation now generates a stochastic hybrid system.
Citation:
Bressloff PC, Lai Y (2011) Stochastic synchronization of neuronal populations with intrinsic and extrinsic noise. The Journal of Mathematical Neuroscience 1: 2. Available: http://dx.doi.org/10.1186/2190-8567-1-2.
Publisher:
Springer Nature
Journal:
The Journal of Mathematical Neuroscience
KAUST Grant Number:
KUK-C1-013-4
Issue Date:
3-May-2011
DOI:
10.1186/2190-8567-1-2
PubMed ID:
22656265
PubMed Central ID:
PMC3280892
Type:
Article
ISSN:
2190-8567
Sponsors:
This publication was based on work supported in part by the National Science Foundation (DMS-0813677) and by Award No KUK-C1-013-4 made by King Abdullah University of Science and Technology (KAUST). PCB was also partially supported by the Royal SocietyWolfson Foundation.
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Full metadata record

DC FieldValue Language
dc.contributor.authorBressloff, Paul Cen
dc.contributor.authorLai, Yi Mingen
dc.date.accessioned2016-02-21T08:51:16Zen
dc.date.available2016-02-21T08:51:16Zen
dc.date.issued2011-05-03en
dc.identifier.citationBressloff PC, Lai Y (2011) Stochastic synchronization of neuronal populations with intrinsic and extrinsic noise. The Journal of Mathematical Neuroscience 1: 2. Available: http://dx.doi.org/10.1186/2190-8567-1-2.en
dc.identifier.issn2190-8567en
dc.identifier.pmid22656265en
dc.identifier.doi10.1186/2190-8567-1-2en
dc.identifier.urihttp://hdl.handle.net/10754/596818en
dc.description.abstractWe extend the theory of noise-induced phase synchronization to the case of a neural master equation describing the stochastic dynamics of an ensemble of uncoupled neuronal population oscillators with intrinsic and extrinsic noise. The master equation formulation of stochastic neurodynamics represents the state of each population by the number of currently active neurons, and the state transitions are chosen so that deterministic Wilson-Cowan rate equations are recovered in the mean-field limit. We apply phase reduction and averaging methods to a corresponding Langevin approximation of the master equation in order to determine how intrinsic noise disrupts synchronization of the population oscillators driven by a common extrinsic noise source. We illustrate our analysis by considering one of the simplest networks known to generate limit cycle oscillations at the population level, namely, a pair of mutually coupled excitatory (E) and inhibitory (I) subpopulations. We show how the combination of intrinsic independent noise and extrinsic common noise can lead to clustering of the population oscillators due to the multiplicative nature of both noise sources under the Langevin approximation. Finally, we show how a similar analysis can be carried out for another simple population model that exhibits limit cycle oscillations in the deterministic limit, namely, a recurrent excitatory network with synaptic depression; inclusion of synaptic depression into the neural master equation now generates a stochastic hybrid system.en
dc.description.sponsorshipThis publication was based on work supported in part by the National Science Foundation (DMS-0813677) and by Award No KUK-C1-013-4 made by King Abdullah University of Science and Technology (KAUST). PCB was also partially supported by the Royal SocietyWolfson Foundation.en
dc.publisherSpringer Natureen
dc.rightsThis is an Open Access article distributed under the terms of the Creative Commons Attribution License (), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.en
dc.rights.urihttp://creativecommons.org/licenses/by/2.0en
dc.titleStochastic synchronization of neuronal populations with intrinsic and extrinsic noise.en
dc.typeArticleen
dc.identifier.journalThe Journal of Mathematical Neuroscienceen
dc.identifier.pmcidPMC3280892en
dc.contributor.institutionMathematical Institute, University of Oxford, 24-29 St. Giles’, Oxford OX1 3LB, UKen
dc.contributor.institutionDepartment of Mathematics, University of Utah, 155 South 1400 East, Salt Lake City, Utah 84112, USAen
kaust.grant.numberKUK-C1-013-4en
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