Pinned fronts in heterogeneous media of jump type

Peter Van Heijster, Arjen Doelman, Tasso J. Kaper, Yasumasa Nishiura, Kei Ichi Ueda

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19 Citations (Scopus)

Abstract

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).

Original languageEnglish
Pages (from-to)127-157
Number of pages31
JournalNonlinearity
Volume24
Issue number1
DOIs
Publication statusPublished - 2011 Jan

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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    Van Heijster, P., Doelman, A., Kaper, T. J., Nishiura, Y., & Ueda, K. I. (2011). Pinned fronts in heterogeneous media of jump type. Nonlinearity, 24(1), 127-157. https://doi.org/10.1088/0951-7715/24/1/007