The stochastic Fitzhugh–Nagumo neuron model in the excitable regime embeds a leaky integrate-and-fire model

In this paper, we provide a complete mathematical construction for a stochastic leaky-integrate-and-fire model (LIF) mimicking the interspike interval (ISI) statistics of a stochastic FitzHugh–Nagumo neuron model (FHN) in the excitable regime, where the unique fixed point is stable. Under specific t...

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Detalles Bibliográficos
Autores principales: Yamakou, Marius E., Tran, Tat Dat, Duc, Luu Hoang, Jost, Jürgen
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2019
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6647150/
https://www.ncbi.nlm.nih.gov/pubmed/31049662
http://dx.doi.org/10.1007/s00285-019-01366-z
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author Yamakou, Marius E.
Tran, Tat Dat
Duc, Luu Hoang
Jost, Jürgen
author_facet Yamakou, Marius E.
Tran, Tat Dat
Duc, Luu Hoang
Jost, Jürgen
author_sort Yamakou, Marius E.
collection PubMed
description In this paper, we provide a complete mathematical construction for a stochastic leaky-integrate-and-fire model (LIF) mimicking the interspike interval (ISI) statistics of a stochastic FitzHugh–Nagumo neuron model (FHN) in the excitable regime, where the unique fixed point is stable. Under specific types of noises, we prove that there exists a global random attractor for the stochastic FHN system. The linearization method is then applied to estimate the firing time and to derive the associated radial equation representing a LIF equation. This result confirms the previous prediction in Ditlevsen and Greenwood (J Math Biol 67(2):239–259, 2013) for the Morris-Lecar neuron model in the bistability regime consisting of a stable fixed point and a stable limit cycle.
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spelling pubmed-66471502019-08-06 The stochastic Fitzhugh–Nagumo neuron model in the excitable regime embeds a leaky integrate-and-fire model Yamakou, Marius E. Tran, Tat Dat Duc, Luu Hoang Jost, Jürgen J Math Biol Article In this paper, we provide a complete mathematical construction for a stochastic leaky-integrate-and-fire model (LIF) mimicking the interspike interval (ISI) statistics of a stochastic FitzHugh–Nagumo neuron model (FHN) in the excitable regime, where the unique fixed point is stable. Under specific types of noises, we prove that there exists a global random attractor for the stochastic FHN system. The linearization method is then applied to estimate the firing time and to derive the associated radial equation representing a LIF equation. This result confirms the previous prediction in Ditlevsen and Greenwood (J Math Biol 67(2):239–259, 2013) for the Morris-Lecar neuron model in the bistability regime consisting of a stable fixed point and a stable limit cycle. Springer Berlin Heidelberg 2019-05-02 2019 /pmc/articles/PMC6647150/ /pubmed/31049662 http://dx.doi.org/10.1007/s00285-019-01366-z Text en © The Author(s) 2019 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Article
Yamakou, Marius E.
Tran, Tat Dat
Duc, Luu Hoang
Jost, Jürgen
The stochastic Fitzhugh–Nagumo neuron model in the excitable regime embeds a leaky integrate-and-fire model
title The stochastic Fitzhugh–Nagumo neuron model in the excitable regime embeds a leaky integrate-and-fire model
title_full The stochastic Fitzhugh–Nagumo neuron model in the excitable regime embeds a leaky integrate-and-fire model
title_fullStr The stochastic Fitzhugh–Nagumo neuron model in the excitable regime embeds a leaky integrate-and-fire model
title_full_unstemmed The stochastic Fitzhugh–Nagumo neuron model in the excitable regime embeds a leaky integrate-and-fire model
title_short The stochastic Fitzhugh–Nagumo neuron model in the excitable regime embeds a leaky integrate-and-fire model
title_sort stochastic fitzhugh–nagumo neuron model in the excitable regime embeds a leaky integrate-and-fire model
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6647150/
https://www.ncbi.nlm.nih.gov/pubmed/31049662
http://dx.doi.org/10.1007/s00285-019-01366-z
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