Traveling waves and global oscillations triggered by attractive molecular interactions in an excitable system
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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.
CitationJohn, K.; Alonso, S.; Bär, M. Traveling waves and global oscillations triggered by attractive molecular interactions in an excitable system. "Physical review E: statistical, nonlinear, and soft matter physics", 17 Novembre 2014, vol. 90, núm. 5, p. 052913-1-052913-7.