Pinned fronts in heterogeneous media of jump type

van Heijster, Peter, Doelman, Arjen , Kaper, Tasso J., Nishiura, Yasumasa , & Ueda, Kei-Ichi (2011) Pinned fronts in heterogeneous media of jump type. Nonlinearity, 24(1), pp. 127-157.

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In this paper, we analyse the impact of a (small) heterogeneity of jump type on the most simple localized solutions of a 3-component FitzHugh–Nagumo-type system. We show that the heterogeneity can pin a 1-front solution, which travels with constant (non-zero) speed in the homogeneous setting, to a fixed, explicitly determined, distance from the heterogeneity. Moreover, we establish the stability of this heterogeneous pinned 1-front solution. In addition, we analyse the pinning of 1-pulse, or 2-front, solutions. The paper is concluded with simulations in which we consider the dynamics and interactions of N-front patterns in domains with M heterogeneities of jump type (N = 3, 4, M ≥ 1).

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7 citations in Scopus
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6 citations in Web of Science®

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ID Code: 55895
Item Type: Journal Article
Refereed: Yes
DOI: 10.1088/0951-7715/24/1/007
ISSN: 0951-7715
Divisions: Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2011 Institute of Physics Publishing Ltd.
Deposited On: 20 Dec 2012 02:10
Last Modified: 11 Jul 2013 02:30

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