Traveling waves and global oscillations triggered by attractive molecular interactions in an excitable system

Karin John, Sergio Alonso, and Markus Bär
Phys. Rev. E 90, 052913 – Published 17 November 2014

Abstract

During pattern formation in spatially extended systems, different mechanisms with different characteristic length scales, e.g., reaction-diffusion processes or molecular interactions, can be active. Such multiscale effects may generate new phenomena, which are not observed in systems where pattern formation occurs on a single scale. Here, we derive and analyze a reaction-diffusion model of the FitzHugh-Nagumo type with short-range attractive molecular interactions of the activator species. The model exhibits a wave instability. Simulations in one and two dimensions show traveling waves with a wavelength set by the parameters of the molecular interaction in the model. In two dimensions, simulations reveal a labyrinthine arrangement of the waves in systems with isotropic diffusion, whereas parallel bands of counterpropagating waves are formed in simulations of a model with anisotropic diffusion. The latter findings are in good qualitative agreement with experimental observation in the catalytic NO+H2 reaction on an anisotropic Rh(110) surface. In addition we have identified a transition regime in the simulations, where a short scale instability triggers global oscillations in an excitable regime.

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  • Received 13 August 2014

DOI:https://doi.org/10.1103/PhysRevE.90.052913

©2014 American Physical Society

Authors & Affiliations

Karin John1,2,*, Sergio Alonso3,†, and Markus Bär3,‡

  • 1Université Grenoble Alpes, LIPhy, F-38000 Grenoble, France
  • 2Centre National de la Recherche Scientifique, LIPhy, F-38000 Grenoble, France
  • 3Physikalisch-Technische Bundesanstalt, Abbestrasse 2–12, D-10587 Berlin, Germany

  • *karin.john@ujf-grenoble.fr
  • sergio.alonso@ptb.de
  • markus.baer@ptb.de

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Issue

Vol. 90, Iss. 5 — November 2014

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