Clarification and Complement to “Mean-Field Description and Propagation of Chaos in Networks of Hodgkin–Huxley and FitzHugh–Nagumo Neurons”

In this note, we clarify the well-posedness of the limit equations to the mean-field N-neuron models proposed in (Baladron et al. in J. Math. Neurosci. 2:10, 2012) and we prove the associated propagation of chaos property. We also complete the modeling issue in (Baladron et al. in J. Math. Neurosci....

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Detalles Bibliográficos
Autores principales: Bossy, Mireille, Faugeras, Olivier, Talay, Denis
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2015
Materias:
Short Report
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4556725/
https://www.ncbi.nlm.nih.gov/pubmed/26329321
http://dx.doi.org/10.1186/s13408-015-0031-8
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author Bossy, Mireille
Faugeras, Olivier
Talay, Denis
author_facet Bossy, Mireille
Faugeras, Olivier
Talay, Denis
author_sort Bossy, Mireille
collection PubMed
description In this note, we clarify the well-posedness of the limit equations to the mean-field N-neuron models proposed in (Baladron et al. in J. Math. Neurosci. 2:10, 2012) and we prove the associated propagation of chaos property. We also complete the modeling issue in (Baladron et al. in J. Math. Neurosci. 2:10, 2012) by discussing the well-posedness of the stochastic differential equations which govern the behavior of the ion channels and the amount of available neurotransmitters.
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spelling pubmed-45567252015-09-09 Clarification and Complement to “Mean-Field Description and Propagation of Chaos in Networks of Hodgkin–Huxley and FitzHugh–Nagumo Neurons” Bossy, Mireille Faugeras, Olivier Talay, Denis J Math Neurosci Short Report In this note, we clarify the well-posedness of the limit equations to the mean-field N-neuron models proposed in (Baladron et al. in J. Math. Neurosci. 2:10, 2012) and we prove the associated propagation of chaos property. We also complete the modeling issue in (Baladron et al. in J. Math. Neurosci. 2:10, 2012) by discussing the well-posedness of the stochastic differential equations which govern the behavior of the ion channels and the amount of available neurotransmitters. Springer Berlin Heidelberg 2015-09-01 /pmc/articles/PMC4556725/ /pubmed/26329321 http://dx.doi.org/10.1186/s13408-015-0031-8 Text en © Bossy et al. 2015 Open Access This 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 Short Report
Bossy, Mireille
Faugeras, Olivier
Talay, Denis
Clarification and Complement to “Mean-Field Description and Propagation of Chaos in Networks of Hodgkin–Huxley and FitzHugh–Nagumo Neurons”
title Clarification and Complement to “Mean-Field Description and Propagation of Chaos in Networks of Hodgkin–Huxley and FitzHugh–Nagumo Neurons”
title_full Clarification and Complement to “Mean-Field Description and Propagation of Chaos in Networks of Hodgkin–Huxley and FitzHugh–Nagumo Neurons”
title_fullStr Clarification and Complement to “Mean-Field Description and Propagation of Chaos in Networks of Hodgkin–Huxley and FitzHugh–Nagumo Neurons”
title_full_unstemmed Clarification and Complement to “Mean-Field Description and Propagation of Chaos in Networks of Hodgkin–Huxley and FitzHugh–Nagumo Neurons”
title_short Clarification and Complement to “Mean-Field Description and Propagation of Chaos in Networks of Hodgkin–Huxley and FitzHugh–Nagumo Neurons”
title_sort clarification and complement to “mean-field description and propagation of chaos in networks of hodgkin–huxley and fitzhugh–nagumo neurons”
topic Short Report
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4556725/
https://www.ncbi.nlm.nih.gov/pubmed/26329321
http://dx.doi.org/10.1186/s13408-015-0031-8
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