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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
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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 (, 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

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