Refractory period in network models of excitable nodes: self-sustaining stable dynamics, extended scaling region and oscillatory behavior

Abstract Networks of excitable nodes have recently attracted much attention particularly in regards to neuronal dynamics, where criticality has been argued to be a fundamental property. Refractory behavior, which limits the excitability of neurons is thought to be an important dynamical property. We...

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Autores principales: S. Amin Moosavi, Afshin Montakhab, Alireza Valizadeh
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Publicado: Nature Portfolio 2017
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spelling oai:doaj.org-article:93d251bde1684bd993399023041542c72021-12-02T11:40:52ZRefractory period in network models of excitable nodes: self-sustaining stable dynamics, extended scaling region and oscillatory behavior10.1038/s41598-017-07135-62045-2322https://doaj.org/article/93d251bde1684bd993399023041542c72017-08-01T00:00:00Zhttps://doi.org/10.1038/s41598-017-07135-6https://doaj.org/toc/2045-2322Abstract Networks of excitable nodes have recently attracted much attention particularly in regards to neuronal dynamics, where criticality has been argued to be a fundamental property. Refractory behavior, which limits the excitability of neurons is thought to be an important dynamical property. We therefore consider a simple model of excitable nodes which is known to exhibit a transition to instability at a critical point (λ = 1), and introduce refractory period into its dynamics. We use mean-field analytical calculations as well as numerical simulations to calculate the activity dependent branching ratio that is useful to characterize the behavior of critical systems. We also define avalanches and calculate probability distribution of their size and duration. We find that in the presence of refractory period the dynamics stabilizes while various parameter regimes become accessible. A sub-critical regime with λ < 1.0, a standard critical behavior with exponents close to critical branching process for λ = 1, a regime with 1 < λ < 2 that exhibits an interesting scaling behavior, and an oscillating regime with λ > 2.0. We have therefore shown that refractory behavior leads to a wide range of scaling as well as periodic behavior which are relevant to real neuronal dynamics.S. Amin MoosaviAfshin MontakhabAlireza ValizadehNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 7, Iss 1, Pp 1-10 (2017)
institution DOAJ
collection DOAJ
language EN
topic Medicine
R
Science
Q
spellingShingle Medicine
R
Science
Q
S. Amin Moosavi
Afshin Montakhab
Alireza Valizadeh
Refractory period in network models of excitable nodes: self-sustaining stable dynamics, extended scaling region and oscillatory behavior
description Abstract Networks of excitable nodes have recently attracted much attention particularly in regards to neuronal dynamics, where criticality has been argued to be a fundamental property. Refractory behavior, which limits the excitability of neurons is thought to be an important dynamical property. We therefore consider a simple model of excitable nodes which is known to exhibit a transition to instability at a critical point (λ = 1), and introduce refractory period into its dynamics. We use mean-field analytical calculations as well as numerical simulations to calculate the activity dependent branching ratio that is useful to characterize the behavior of critical systems. We also define avalanches and calculate probability distribution of their size and duration. We find that in the presence of refractory period the dynamics stabilizes while various parameter regimes become accessible. A sub-critical regime with λ < 1.0, a standard critical behavior with exponents close to critical branching process for λ = 1, a regime with 1 < λ < 2 that exhibits an interesting scaling behavior, and an oscillating regime with λ > 2.0. We have therefore shown that refractory behavior leads to a wide range of scaling as well as periodic behavior which are relevant to real neuronal dynamics.
format article
author S. Amin Moosavi
Afshin Montakhab
Alireza Valizadeh
author_facet S. Amin Moosavi
Afshin Montakhab
Alireza Valizadeh
author_sort S. Amin Moosavi
title Refractory period in network models of excitable nodes: self-sustaining stable dynamics, extended scaling region and oscillatory behavior
title_short Refractory period in network models of excitable nodes: self-sustaining stable dynamics, extended scaling region and oscillatory behavior
title_full Refractory period in network models of excitable nodes: self-sustaining stable dynamics, extended scaling region and oscillatory behavior
title_fullStr Refractory period in network models of excitable nodes: self-sustaining stable dynamics, extended scaling region and oscillatory behavior
title_full_unstemmed Refractory period in network models of excitable nodes: self-sustaining stable dynamics, extended scaling region and oscillatory behavior
title_sort refractory period in network models of excitable nodes: self-sustaining stable dynamics, extended scaling region and oscillatory behavior
publisher Nature Portfolio
publishDate 2017
url https://doaj.org/article/93d251bde1684bd993399023041542c7
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