Chimera states on a flat torus.

Chimera states are surprising spatiotemporal patterns in which regions of coherence and incoherence coexist. Initially observed numerically, 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 "spot" and "stripe" chimeras (similar to those observed in experiments) can exist in a periodic space. We also discover a previously unobserved asymmetric chimera state, whose existence plays a major role in determining when other chimera states are observable in experiment and simulation. Finally, we use numerical methods to verify theoretical predictions and determine which states are dynamically stable.