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Neural Excitability and Singular Bifurcations.

Authors
  • De Maesschalck, Peter
  • Wechselberger, Martin
Type
Published Article
Journal
The Journal of Mathematical Neuroscience
Publisher
Springer (Biomed Central Ltd.)
Publication Date
Dec 01, 2015
Volume
5
Issue
1
Pages
29–29
Identifiers
DOI: 10.1186/s13408-015-0029-2
PMID: 26246435
Source
Medline
License
Unknown

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.

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