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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
Citation: 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.
URI: http://hdl.handle.net/1942/20401
DOI: 10.1186/s13408-015-0029-2
ISI #: 000366609100001
ISSN: 2190-8567
Category: A1
Type: Journal Contribution
Appears in Collections: Research publications

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