title: Traveling waves and global oscillations triggered by attractive molecular interactions in an excitable system.
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+H_{2} 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.
authors.affiliation: Université Grenoble Alpes, LIPhy, F-38000 Grenoble, France and Centre National de la Recherche Scientifique, LIPhy, F-38000 Grenoble, France.
authors.forename: Karin
authors.initials: K
authors.lastname: John
authors.affiliation: Physikalisch-Technische Bundesanstalt, Abbestrasse 2-12, D-10587 Berlin, Germany.
authors.forename: Sergio
authors.initials: S
authors.lastname: Alonso
authors.affiliation: Physikalisch-Technische Bundesanstalt, Abbestrasse 2-12, D-10587 Berlin, Germany.
authors.forename: Markus
authors.initials: M
authors.lastname: Bär