Complex oscillations in the delayed Fitzhugh-Nagumo equation
type: Item
instance of: scholarly article
title: Complex oscillations in the delayed Fitzhugh-Nagumo equation
zbMATH Open document ID: 1337.34079
author: M. Krupa
author: Jonathan D. Touboul
published in: Journal of Nonlinear Science
publication date: 2016-03-01T00:00:00Z
review text: The paper considers the bifurcations in the FitzHugh-Nagumo system with delayed feedback \[ \begin{aligned} x'(t) & = x(t)-\frac{1}{3}x^{3}(t)+y(t)+J(x(t)-x(t-\tau)),\\ y'(t) & = \varepsilon(a-x(t)),\end{aligned} \] where \(J,a\), and \(\varepsilon\ll 1\) are parameters. A detailed analytical study of the bifurcations of steady states is presented. This includes families of Hopf bifurcations for various values of parameters and time-delay \(\tau\) as well as Bogdanov-Takens condimension-2 bifurcation. Additionally, a numerical bifurcation analysis is given that conjectures a variety of complex oscillations in the system such as regular bursting, chaotic bursting or torus canards.
reviewed by: S. Yanchuk
Mathematics Subject Classification ID: 34K60
Mathematics Subject Classification ID: 34K26
Mathematics Subject Classification ID: 34K23
Mathematics Subject Classification ID: 34K18
Mathematics Subject Classification ID: 92C20
Mathematics Subject Classification ID: 34K13
zbMATH DE Number: 6547871
zbMATH Keywords: delayed differential equations
zbMATH Keywords: slow-fast systems
zbMATH Keywords: mixed-mode oscillations
zbMATH Keywords: bursting
zbMATH Keywords: chaos
describes a project that uses: Maple
describes a project that uses: DDE-BIFTOOL
MaRDI profile type: Publication
full work available at URL: s00332-015-9268-3
OpenAlex ID: W1610445876
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DOI: 10.1007/S00332-015-9268-3
description: scientific article; zbMATH DE number 6547871