Bifurcations to travelling planar spots in a three-component FitzHugh-Nagumo system

van Heijster, Peter & Sandstede, Björn (2014) Bifurcations to travelling planar spots in a three-component FitzHugh-Nagumo system. Physica D : Nonlinear Phenomena, 275, pp. 19-34.

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Abstract

In this article, we analyse bifurcations from stationary stable spots to travelling spots in a planar three-component FitzHugh-Nagumo system that was proposed previously as a phenomenological model of gas-discharge systems. By combining formal analyses, center-manifold reductions, and detailed numerical continuation studies, we show that, in the parameter regime under consideration, the stationary spot destabilizes either through its zeroth Fourier mode in a Hopf bifurcation or through its first Fourier mode in a pitchfork or drift bifurcation, whilst the remaining Fourier modes appear to create only secondary bifurcations. Pitchfork bifurcations result in travelling spots, and we derive criteria for the criticality of these bifurcations. Our main finding is that supercritical drift bifurcations, leading to stable travelling spots, arise in this model, which does not seem possible for its two-component version.

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ID Code: 67122
Item Type: Journal Article
Refereed: Yes
Keywords: FitzHugh–Nagumo system, Planar localized structures, Travelling spots, Bifurcations
DOI: 10.1016/j.physd.2014.02.001
ISSN: 0167-2789
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > PURE MATHEMATICS (010100) > Ordinary Differential Equations Difference Equations and Dynamical Systems (010109)
Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > PURE MATHEMATICS (010100) > Partial Differential Equations (010110)
Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200) > Dynamical Systems in Applications (010204)
Divisions: Current > Schools > School of Mathematical Sciences
Copyright Owner: Copyright 2014 Elsevier B.V.
Copyright Statement: This is the author’s version of a work that was accepted for publication in Physica D : Nonlinear Phenomena. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Physica D : Nonlinear Phenomena, [Volume 275, (1 May 2014)] DOI: 10.1016/j.physd.2014.02.001
Deposited On: 10 Feb 2014 22:34
Last Modified: 11 May 2016 05:31

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