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Weak-noise-induced transitions with inhibition and modulation of neural oscillations

We analyze the effect of weak-noise-induced transitions on the dynamics of the FitzHugh–Nagumo neuron model in a bistable state consisting of a stable fixed point and a stable unforced limit cycle. Bifurcation and slow-fast analysis give conditions on the parameter space for the establishment of thi...

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Autores principales: Yamakou, Marius E., Jost, Jürgen
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2018
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6153713/
https://www.ncbi.nlm.nih.gov/pubmed/29995240
http://dx.doi.org/10.1007/s00422-018-0770-1
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author Yamakou, Marius E.
Jost, Jürgen
author_facet Yamakou, Marius E.
Jost, Jürgen
author_sort Yamakou, Marius E.
collection PubMed
description We analyze the effect of weak-noise-induced transitions on the dynamics of the FitzHugh–Nagumo neuron model in a bistable state consisting of a stable fixed point and a stable unforced limit cycle. Bifurcation and slow-fast analysis give conditions on the parameter space for the establishment of this bi-stability. In the parametric zone of bi-stability, weak-noise amplitudes may strongly inhibit the neuron’s spiking activity. Surprisingly, increasing the noise strength leads to a minimum in the spiking activity, after which the activity starts to increase monotonically with an increase in noise strength. We investigate this inhibition and modulation of neural oscillations by weak-noise amplitudes by looking at the variation of the mean number of spikes per unit time with the noise intensity. We show that this phenomenon always occurs when the initial conditions lie in the basin of attraction of the stable limit cycle. For initial conditions in the basin of attraction of the stable fixed point, the phenomenon, however, disappears, unless the timescale separation parameter of the model is bounded within some interval. We provide a theoretical explanation of this phenomenon in terms of the stochastic sensitivity functions of the attractors and their minimum Mahalanobis distances from the separatrix isolating the basins of attraction.
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spelling pubmed-61537132018-10-04 Weak-noise-induced transitions with inhibition and modulation of neural oscillations Yamakou, Marius E. Jost, Jürgen Biol Cybern Original Article We analyze the effect of weak-noise-induced transitions on the dynamics of the FitzHugh–Nagumo neuron model in a bistable state consisting of a stable fixed point and a stable unforced limit cycle. Bifurcation and slow-fast analysis give conditions on the parameter space for the establishment of this bi-stability. In the parametric zone of bi-stability, weak-noise amplitudes may strongly inhibit the neuron’s spiking activity. Surprisingly, increasing the noise strength leads to a minimum in the spiking activity, after which the activity starts to increase monotonically with an increase in noise strength. We investigate this inhibition and modulation of neural oscillations by weak-noise amplitudes by looking at the variation of the mean number of spikes per unit time with the noise intensity. We show that this phenomenon always occurs when the initial conditions lie in the basin of attraction of the stable limit cycle. For initial conditions in the basin of attraction of the stable fixed point, the phenomenon, however, disappears, unless the timescale separation parameter of the model is bounded within some interval. We provide a theoretical explanation of this phenomenon in terms of the stochastic sensitivity functions of the attractors and their minimum Mahalanobis distances from the separatrix isolating the basins of attraction. Springer Berlin Heidelberg 2018-07-11 2018 /pmc/articles/PMC6153713/ /pubmed/29995240 http://dx.doi.org/10.1007/s00422-018-0770-1 Text en © The Author(s) 2018 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 Original Article
Yamakou, Marius E.
Jost, Jürgen
Weak-noise-induced transitions with inhibition and modulation of neural oscillations
title Weak-noise-induced transitions with inhibition and modulation of neural oscillations
title_full Weak-noise-induced transitions with inhibition and modulation of neural oscillations
title_fullStr Weak-noise-induced transitions with inhibition and modulation of neural oscillations
title_full_unstemmed Weak-noise-induced transitions with inhibition and modulation of neural oscillations
title_short Weak-noise-induced transitions with inhibition and modulation of neural oscillations
title_sort weak-noise-induced transitions with inhibition and modulation of neural oscillations
topic Original Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6153713/
https://www.ncbi.nlm.nih.gov/pubmed/29995240
http://dx.doi.org/10.1007/s00422-018-0770-1
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