Neural Excitability and Singular Bifurcations

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• 作者：Peter De Maesschalck…
• 关键词：Bifurcation theory ; Canards ; Excitability ; Geometric singular perturbation theory ; Neural dynamics
• 刊名：The Journal of Mathematical Neuroscience (JMN)
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：5
• 期：1
• 全文大小：1,113 KB
• 刊物主题：Mathematical Modeling and Industrial Mathematics; Neurosciences; Applications of Mathematics;
• 出版者：Springer Berlin Heidelberg
• ISSN：2190-8567

文摘

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.