title: Chimera states on a flat torus.
abstract: 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.
authors.affiliation: Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, Illinois 60208, USA. markpanaggio2014@u.northwestern.edu
authors.forename: Mark J
authors.initials: MJ
authors.lastname: Panaggio
authors.forename: Daniel M
authors.initials: DM
authors.lastname: Abrams