We study two-layer networks of identical phase oscillators. Each individual layer is a ring network for which a non-local intra-layer coupling leads to the formation of a chimera state. The number of oscillators and their natural frequencies is in general different across the layers. We couple the phases of individual oscillators in one layer to the phase of the mean field of the other layer. This coupling from the mean field to individual oscillators is done in both directions. For a sufficient strength of this interlayer coupling, the phases of the mean fields lock across the two layers. In contrast, both layers continue to exhibit chimera states with no locking between the phases of individual oscillators across layers, and the two mean field amplitudes remain uncorrelated. Hence, the networks’ mean fields show phase synchronization which is analogous to the one between low-dimensional chaotic oscillators. The required coupling strength to achieve this mean field phase synchronization increases with the mismatches in the network sizes and the oscillators’ natural frequencies.

We acknowledge funding from the Spanish Ministry of Economy and Competitiveness, Grant FIS2014-54177-R (R.G.A and G.R.), the CERCA Programme of the Generalitat de Catalunya (R.G.A), the European Unions Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 642563 (R.G.A and I.M.) and by the DFG in the framework of SFB 910 (E.S., A.Z. and G.R.).