Planar radial spots in a three-component FitzHugh-Nagumo system

van Heijster, Peter & Sandstede, Bjorn (2011) Planar radial spots in a three-component FitzHugh-Nagumo system. Journal of Nonlinear Science, 21(5), pp. 705-745.

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Abstract

Localized planar patterns arise in many reaction-diffusion models. Most of the paradigm equations that have been studied so far are two-component models. While stationary localized structures are often found to be stable in such systems, travelling patterns either do not exist or are found to be unstable. In contrast, numerical simulations indicate that localized travelling structures can be stable in three-component systems. As a first step towards explaining this phenomenon, a planar singularly perturbed three-component reaction-diffusion system that arises in the context of gas-discharge systems is analysed in this paper. Using geometric singular perturbation theory, the existence and stability regions of radially symmetric stationary spot solutions are delineated and, in particular, stable spots are shown to exist in appropriate parameter regimes. This result opens up the possibility of identifying and analysing drift and Hopf bifurcations, and their criticality, from the stationary spots described here.

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16 citations in Scopus
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13 citations in Web of Science®

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ID Code: 55893
Item Type: Journal Article
Refereed: Yes
Keywords: FitzHugh-Nagumo system, Planar localized structures, Geometrical singular perturbation theory, Stability analysis
DOI: 10.1007/s00332-011-9098-x
ISSN: 0938-8974
Divisions: Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2011 Springer
Deposited On: 20 Dec 2012 02:13
Last Modified: 11 Jul 2013 02:14

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