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The notion of a weak chimeras provides a tractable definition for chimerastates in networks of finitely many phase oscillators. Here we generalize thedefinition of a weak chimera to a more general class of equivariant dynamicalsystems by characterizing solutions in terms of the isotropy of their angularfrequency vector - for coupled phase oscillators the angular frequency vectoris given by the average of the vector field along a trajectory. Symmetries ofsolutions automatically imply angular frequency synchronization. We show thatthe presence of such symmetries is not necessary by giving a result for theexistence of weak chimeras without instantaneous or setwise symmetries forcoupled phase oscillators. Moreover, we construct a coupling function thatgives rise to chaotic weak chimeras without symmetry in weakly coupledpopulations of phase oscillators with generalized coupling.

Isotropy of Angular Frequencies and Weak Chimeras With Broken Symmetry