Cluster formation, standing waves, and stripe patterns in oscillatory active media with local and global coupling

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Abstract
In recent years, the effect of global coupling on spatiotemporal pattern formation in oscillatory media has attracted considerable interest. For the complex Ginzburg-Landau equation, modified by a global coupling term, we derive a criterion for cluster formation and discuss standing wave solutions with an intrinsic wavelength in the Benjamin-Feir stable parameter range. We argue that clustering expresses the dominance of global coupling. In two-dimensional media the interplay between the standing wave instability and anisotropic diffusion may generate stripe patterns coupled to a spatially uniform oscillating mode. Then, by direct numerical simulation, we show that the globally coupled reconstruction model—proposed by Krischer, Eiswirth, and Ertl for CO oxidation on Pt(110) [Surf. Sci. 900, 251 (1991)]—exhibits clustering and predicts the presence of standing waves with an intrinsic wavelength.