Coherent Structures Generated by Inhomogeneities in Oscillatory Media

We investigate the effect of spatially localized inhomogeneities on a spatially homogeneous oscillation in a reaction-diffusion system. In dimension up to 2, 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 2 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.