Complex oscillations in the delayed Fitzhugh-Nagumo equation
Dynamical Systems
2016-02-17 v4
Abstract
Motivated by the dynamics of neuronal responses, we analyze the dynamics of the Fitzhugh-Nagumo slow-fast system with delayed self-coupling. This system provides a canonical example of a canard explosion for sufficiently small delays. Beyond this regime, delays significantly enrich the dynamics, leading to mixed-mode oscillations, bursting and chaos. These behaviors emerge from a delay-induced subcritical Bogdanov-Takens instability arising at the fold points of the S-shaped critical manifold. Underlying the transition from canard-induced to delay-induced dynamics is an abrupt switch in the nature of the Hopf bifurcation.
Cite
@article{arxiv.1404.5841,
title = {Complex oscillations in the delayed Fitzhugh-Nagumo equation},
author = {Maciej Krupa and Jonathan Touboul},
journal= {arXiv preprint arXiv:1404.5841},
year = {2016}
}