Coherent Structures Generated by Inhomogeneities in Oscillatory Media

Abstract

We investigate the effect of spatially localized inhomogeneities on a spatially homogeneous oscillation in a reaction‐diffusion system. In dimension up to two, we find sources and contact defects, that is, the inhomogeneity may either send out phase waves or act as a weak sink. We show that small inhomogeneities cannot act as sources in more than two space dimensions. We also derive asymptotics for wavenumbers and group velocities in the far field. The results are established rigorously for radially symmetric inhomogeneities in reaction‐diffusion systems, and for arbitrary inhomogeneities in a modulation equation approximation.