Chimeras in globally coupled oscillatory systems: From ensembles of oscillators to spatially continuous media

Abstract: We study an oscillatory medium with a nonlinear global coupling that gives rise to a harmonic mean-field oscillation with constant amplitude and frequency. Two types of cluster states are found, each undergoing a symmetry-breaking transition towards a related chimera state. We demonstrate that the diffusional coupling is non-essential for these complex dynamics. Furthermore, we investigate localized turbulence and discuss whether it can be categorized as a chimera state.