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The geometry of rest–spike bistability

Morris–Lecar model is arguably the simplest dynamical model that retains both the slow–fast geometry of excitable phase portraits and the physiological interpretation of a conductance-based model. We augment this model with one slow inward current to capture the additional property of bistability be...

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Autores principales: Cirillo, Giuseppe Ilario, Sepulchre, Rodolphe
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2020
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7474052/
https://www.ncbi.nlm.nih.gov/pubmed/32886221
http://dx.doi.org/10.1186/s13408-020-00090-z
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author Cirillo, Giuseppe Ilario
Sepulchre, Rodolphe
author_facet Cirillo, Giuseppe Ilario
Sepulchre, Rodolphe
author_sort Cirillo, Giuseppe Ilario
collection PubMed
description Morris–Lecar model is arguably the simplest dynamical model that retains both the slow–fast geometry of excitable phase portraits and the physiological interpretation of a conductance-based model. We augment this model with one slow inward current to capture the additional property of bistability between a resting state and a spiking limit cycle for a range of input current. The resulting dynamical system is a core structure for many dynamical phenomena such as slow spiking and bursting. We show how the proposed model combines physiological interpretation and mathematical tractability and we discuss the benefits of the proposed approach with respect to alternative models in the literature.
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spelling pubmed-74740522020-09-16 The geometry of rest–spike bistability Cirillo, Giuseppe Ilario Sepulchre, Rodolphe J Math Neurosci Research Morris–Lecar model is arguably the simplest dynamical model that retains both the slow–fast geometry of excitable phase portraits and the physiological interpretation of a conductance-based model. We augment this model with one slow inward current to capture the additional property of bistability between a resting state and a spiking limit cycle for a range of input current. The resulting dynamical system is a core structure for many dynamical phenomena such as slow spiking and bursting. We show how the proposed model combines physiological interpretation and mathematical tractability and we discuss the benefits of the proposed approach with respect to alternative models in the literature. Springer Berlin Heidelberg 2020-09-04 /pmc/articles/PMC7474052/ /pubmed/32886221 http://dx.doi.org/10.1186/s13408-020-00090-z Text en © The Author(s) 2020 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
spellingShingle Research
Cirillo, Giuseppe Ilario
Sepulchre, Rodolphe
The geometry of rest–spike bistability
title The geometry of rest–spike bistability
title_full The geometry of rest–spike bistability
title_fullStr The geometry of rest–spike bistability
title_full_unstemmed The geometry of rest–spike bistability
title_short The geometry of rest–spike bistability
title_sort geometry of rest–spike bistability
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7474052/
https://www.ncbi.nlm.nih.gov/pubmed/32886221
http://dx.doi.org/10.1186/s13408-020-00090-z
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