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A Complex-Valued Firing-Rate Model That Approximates the Dynamics of Spiking Networks

Firing-rate models provide an attractive approach for studying large neural networks because they can be simulated rapidly and are amenable to mathematical analysis. Traditional firing-rate models assume a simple form in which the dynamics are governed by a single time constant. These models fail to...

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Detalles Bibliográficos
Autores principales: Schaffer, Evan S., Ostojic, Srdjan, Abbott, L. F.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Public Library of Science 2013
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3814717/
https://www.ncbi.nlm.nih.gov/pubmed/24204236
http://dx.doi.org/10.1371/journal.pcbi.1003301
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author Schaffer, Evan S.
Ostojic, Srdjan
Abbott, L. F.
author_facet Schaffer, Evan S.
Ostojic, Srdjan
Abbott, L. F.
author_sort Schaffer, Evan S.
collection PubMed
description Firing-rate models provide an attractive approach for studying large neural networks because they can be simulated rapidly and are amenable to mathematical analysis. Traditional firing-rate models assume a simple form in which the dynamics are governed by a single time constant. These models fail to replicate certain dynamic features of populations of spiking neurons, especially those involving synchronization. We present a complex-valued firing-rate model derived from an eigenfunction expansion of the Fokker-Planck equation and apply it to the linear, quadratic and exponential integrate-and-fire models. Despite being almost as simple as a traditional firing-rate description, this model can reproduce firing-rate dynamics due to partial synchronization of the action potentials in a spiking model, and it successfully predicts the transition to spike synchronization in networks of coupled excitatory and inhibitory neurons.
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spelling pubmed-38147172013-11-07 A Complex-Valued Firing-Rate Model That Approximates the Dynamics of Spiking Networks Schaffer, Evan S. Ostojic, Srdjan Abbott, L. F. PLoS Comput Biol Research Article Firing-rate models provide an attractive approach for studying large neural networks because they can be simulated rapidly and are amenable to mathematical analysis. Traditional firing-rate models assume a simple form in which the dynamics are governed by a single time constant. These models fail to replicate certain dynamic features of populations of spiking neurons, especially those involving synchronization. We present a complex-valued firing-rate model derived from an eigenfunction expansion of the Fokker-Planck equation and apply it to the linear, quadratic and exponential integrate-and-fire models. Despite being almost as simple as a traditional firing-rate description, this model can reproduce firing-rate dynamics due to partial synchronization of the action potentials in a spiking model, and it successfully predicts the transition to spike synchronization in networks of coupled excitatory and inhibitory neurons. Public Library of Science 2013-10-31 /pmc/articles/PMC3814717/ /pubmed/24204236 http://dx.doi.org/10.1371/journal.pcbi.1003301 Text en © 2013 Schaffer et al http://creativecommons.org/licenses/by/4.0/ 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 author and source are properly credited.
spellingShingle Research Article
Schaffer, Evan S.
Ostojic, Srdjan
Abbott, L. F.
A Complex-Valued Firing-Rate Model That Approximates the Dynamics of Spiking Networks
title A Complex-Valued Firing-Rate Model That Approximates the Dynamics of Spiking Networks
title_full A Complex-Valued Firing-Rate Model That Approximates the Dynamics of Spiking Networks
title_fullStr A Complex-Valued Firing-Rate Model That Approximates the Dynamics of Spiking Networks
title_full_unstemmed A Complex-Valued Firing-Rate Model That Approximates the Dynamics of Spiking Networks
title_short A Complex-Valued Firing-Rate Model That Approximates the Dynamics of Spiking Networks
title_sort complex-valued firing-rate model that approximates the dynamics of spiking networks
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3814717/
https://www.ncbi.nlm.nih.gov/pubmed/24204236
http://dx.doi.org/10.1371/journal.pcbi.1003301
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