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arXiv · 1404.5841

Complex oscillations in the delayed Fitzhugh-Nagumo equation

Maciej Krupa·Jonathan Touboul
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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.

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Maciej Krupa, Jonathan Touboul. 2014-04-23. Complex oscillations in the delayed Fitzhugh-Nagumo equation. https://doi.org/10.1007/s00332-015-9272-7

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