Stochastic synchronization of neuronal populations with intrinsic and extrinsic noise.
KAUST Grant NumberKUK-C1-013-4
Online Publication Date2011-05-04
Print Publication Date2011
Permanent link to this recordhttp://hdl.handle.net/10754/596818
MetadataShow full item record
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.
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.
SponsorsThis 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.
PubMed Central IDPMC3280892
CollectionsPublications Acknowledging KAUST Support
Except where otherwise noted, this item's license is described as This 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.
- Metastable states and quasicycles in a stochastic Wilson-Cowan model of neuronal population dynamics.
- Authors: Bressloff PC
- Issue date: 2010 Nov
- Robust synchronization control scheme of a population of nonlinear stochastic synthetic genetic oscillators under intrinsic and extrinsic molecular noise via quorum sensing.
- Authors: Chen BS, Hsu CY
- Issue date: 2012 Oct 26
- Path-integral methods for analyzing the effects of fluctuations in stochastic hybrid neural networks.
- Authors: Bressloff PC
- Issue date: 2015
- Brain rhythm bursts are enhanced by multiplicative noise.
- Authors: Powanwe AS, Longtin A
- Issue date: 2021 Jan
- Laws of large numbers and langevin approximations for stochastic neural field equations.
- Authors: Riedler MG, Buckwar E
- Issue date: 2013 Jan 23