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

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.