Critical behaviour of the stochastic Wilson-Cowan model.

Spontaneous brain activity is characterized by bursts and avalanche-like dynamics, with scale-free features typical of critical behaviour. The stochastic version of the celebrated Wilson-Cowan model has been widely studied as a system of spiking neurons reproducing non-trivial features of the neural...

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Autores principales:	Antonio de Candia, Alessandro Sarracino, Ilenia Apicella, Lucilla de Arcangelis
Formato:	article
Lenguaje:	EN
Publicado:	Public Library of Science (PLoS) 2021
Materias:	Biology (General) QH301-705.5
Acceso en línea:	https://doaj.org/article/bb8970e19e1b4016966430b3085e058b
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spelling	oai:doaj.org-article:bb8970e19e1b4016966430b3085e058b2021-12-02T19:58:00ZCritical behaviour of the stochastic Wilson-Cowan model.1553-734X1553-735810.1371/journal.pcbi.1008884https://doaj.org/article/bb8970e19e1b4016966430b3085e058b2021-08-01T00:00:00Zhttps://doi.org/10.1371/journal.pcbi.1008884https://doaj.org/toc/1553-734Xhttps://doaj.org/toc/1553-7358Spontaneous brain activity is characterized by bursts and avalanche-like dynamics, with scale-free features typical of critical behaviour. The stochastic version of the celebrated Wilson-Cowan model has been widely studied as a system of spiking neurons reproducing non-trivial features of the neural activity, from avalanche dynamics to oscillatory behaviours. However, to what extent such phenomena are related to the presence of a genuine critical point remains elusive. Here we address this central issue, providing analytical results in the linear approximation and extensive numerical analysis. In particular, we present results supporting the existence of a bona fide critical point, where a second-order-like phase transition occurs, characterized by scale-free avalanche dynamics, scaling with the system size and a diverging relaxation time-scale. Moreover, our study shows that the observed critical behaviour falls within the universality class of the mean-field branching process, where the exponents of the avalanche size and duration distributions are, respectively, 3/2 and 2. We also provide an accurate analysis of the system behaviour as a function of the total number of neurons, focusing on the time correlation functions of the firing rate in a wide range of the parameter space.Antonio de CandiaAlessandro SarracinoIlenia ApicellaLucilla de ArcangelisPublic Library of Science (PLoS)articleBiology (General)QH301-705.5ENPLoS Computational Biology, Vol 17, Iss 8, p e1008884 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Biology (General) QH301-705.5
spellingShingle	Biology (General) QH301-705.5 Antonio de Candia Alessandro Sarracino Ilenia Apicella Lucilla de Arcangelis Critical behaviour of the stochastic Wilson-Cowan model.
description	Spontaneous brain activity is characterized by bursts and avalanche-like dynamics, with scale-free features typical of critical behaviour. The stochastic version of the celebrated Wilson-Cowan model has been widely studied as a system of spiking neurons reproducing non-trivial features of the neural activity, from avalanche dynamics to oscillatory behaviours. However, to what extent such phenomena are related to the presence of a genuine critical point remains elusive. Here we address this central issue, providing analytical results in the linear approximation and extensive numerical analysis. In particular, we present results supporting the existence of a bona fide critical point, where a second-order-like phase transition occurs, characterized by scale-free avalanche dynamics, scaling with the system size and a diverging relaxation time-scale. Moreover, our study shows that the observed critical behaviour falls within the universality class of the mean-field branching process, where the exponents of the avalanche size and duration distributions are, respectively, 3/2 and 2. We also provide an accurate analysis of the system behaviour as a function of the total number of neurons, focusing on the time correlation functions of the firing rate in a wide range of the parameter space.
format	article
author	Antonio de Candia Alessandro Sarracino Ilenia Apicella Lucilla de Arcangelis
author_facet	Antonio de Candia Alessandro Sarracino Ilenia Apicella Lucilla de Arcangelis
author_sort	Antonio de Candia
title	Critical behaviour of the stochastic Wilson-Cowan model.
title_short	Critical behaviour of the stochastic Wilson-Cowan model.
title_full	Critical behaviour of the stochastic Wilson-Cowan model.
title_fullStr	Critical behaviour of the stochastic Wilson-Cowan model.
title_full_unstemmed	Critical behaviour of the stochastic Wilson-Cowan model.
title_sort	critical behaviour of the stochastic wilson-cowan model.
publisher	Public Library of Science (PLoS)
publishDate	2021
url	https://doaj.org/article/bb8970e19e1b4016966430b3085e058b
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Critical behaviour of the stochastic Wilson-Cowan model.

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