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.
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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|Item Type:||Journal Article|
|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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