  Discovered numerically by Kuramoto and Battogtokh in 2002, chimera states are
spatiotemporal patterns in which regions of coherence and incoherence coexist.
These mathematical oddities were recently reproduced in a laboratory setting
sparking a flurry of interest in their properties. Here we use asymptotic
methods to derive the conditions under which two-dimensional chimeras, similar
to those observed in the experiments, can appear in a periodic space. We also
use numerical integration to explore the dynamics of these chimeras and
determine which are dynamically stable.
