  Biological and physical systems that can be classified as oscillatory media
give rise to interesting phenomena like target patterns and spiral waves. The
existence of these structures has been proven in the case of systems with local
diffusive interactions. In this paper the more general case of oscillatory
media with nonlocal coupling is considered. We model these systems using
evolution equations where the nonlocal interactions are expressed via a
diffusive convolution kernel, and prove the existence of rotating wave
solutions for these systems. Since the nonlocal nature of the equations
precludes the use of standard techniques from spatial dynamics, the method we
use relies instead on a combination of a multiple-scales analysis and a
construction similar to Lyapunov-Schmidt. This approach then allows us to
derive a normal form, or reduced equation, that captures the leading order
behavior of these solutions.
