## Rotating waves: from local discrete systems to nonlocal continuous media

bard@pitt.edu

University of Pittsburgh

In two or more spatial dimensions, oscillatory and excitable media are able to produce spiral and other types of rotating behavior. We start with a system of locally coupled phase oscillators on an NxN grid and show that when the coupling includes non-odd components, spiral waves emerge. We show that as $N\to\infty$, that the dynamics can be understood by a Burgers type equation on an annulus with inner radius proportional to 1/N. We then turn to nonlocal coupling on an annulus and show that rotating waves solve a certain one-dimensional integral equation. We investigate the stability of the waves and connect an instability as the inner radius of the annulus shrinks to the formation of so-called chimeras.