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 language | English |
|---|---|
| Pages (from-to) | 127-157 |
| Number of pages | 31 |
| Journal | Nonlinearity |
| Volume | 24 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 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