Please use this identifier to cite or link to this item:
http://hdl.handle.net/1942/20401
Title: | Neural Excitability and Singular Bifurcations | Authors: | DE MAESSCHALCK, Peter Wechselberger, Martin |
Issue Date: | 2015 | Source: | Journal of Mathematical Neuroscience, 5 (16), p. 1-32 | Abstract: | We discuss the notion of excitability in 2D slow/fast neural models from a geometric singular perturbation theory point of view. We focus on the inherent singular nature of slow/fast neural models and define excitability via singular bifurcations. In particular, we show that type I excitability is associated with a novel singular Bogdanov–Takens/SNIC bifurcation while type II excitability is associated with a singular Andronov–Hopf bifurcation. In both cases, canards play an important role in the understanding of the unfolding of these singular bifurcation structures. We also explain the transition between the two excitability types and highlight all bifurcations involved, thus providing a complete analysis of excitability based on geometric singular perturbation theory. | Keywords: | bifurcation theory; canards; excitability; geometric singular perturbation theory; neural dynamics | Document URI: | http://hdl.handle.net/1942/20401 | ISSN: | 2190-8567 | e-ISSN: | 2190-8567 | DOI: | 10.1186/s13408-015-0029-2 | ISI #: | 000366609100001 | Rights: | © 2015 De Maesschalck and Wechselberger. 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. | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2021 |
Appears in Collections: | Research publications |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
s13408-015-0029-2.pdf | Published version | 1.11 MB | Adobe PDF | View/Open |
SCOPUSTM
Citations
13
checked on Sep 3, 2020
WEB OF SCIENCETM
Citations
31
checked on Sep 29, 2024
Page view(s)
72
checked on Sep 7, 2022
Download(s)
110
checked on Sep 7, 2022
Google ScholarTM
Check
Altmetric
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.