Neural Excitability and Singular Bifurcations

11Citations
Citations of this article
24Readers
Mendeley users who have this article in their library.

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.

Cite

CITATION STYLE

APA

De Maesschalck, P., & Wechselberger, M. (2015). Neural Excitability and Singular Bifurcations. Journal of Mathematical Neuroscience, 5(1). https://doi.org/10.1186/s13408-015-0029-2

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free