Networks of coupled oscillators in chimera states are characterized by an intriguing interplay of synchronous and asynchronous motion. While chimera states were initially discovered in mathematical model systems, there is growing experimental and conceptual evidence that they manifest themselves also in natural and man-made networks. In real-world systems, however, synchronization and desynchronization are not only important within individual networks but also across different interacting networks. It is therefore essential to investigate if chimera states can be synchronized across networks. To address this open problem, we use the classical setting of ring networks of non-locally coupled identical phase oscillators. We apply diffusive drive-response couplings between pairs of such networks that individually show chimera states when there is no coupling between them. The drive and response networks are either identical or they differ by a variable mismatch in their phase lag parameters. In both cases, already for weak couplings, the coherent domain of the response network aligns its position to the one of the driver networks. For identical networks, a sufficiently strong coupling leads to identical synchronization between the drive and response. For non-identical networks, we use the auxiliary system approach to demonstrate that generalized synchronization is established instead. In this case, the response network continues to show a chimera dynamics which however remains distinct from the one of the driver. Hence, segregated synchronized and desynchronized domains in individual networks congregate in generalized synchronization across networks. Published by AIP Publishing. Notwithstanding their simple structure, networks of coupled oscillators can show intriguingly complex dynamics. In a classical setting, 1 identical phase oscillators are arranged on a ring and are connected by a nonlocal coupling, which has the same form for all oscillators. Despite this translational symmetry of the network, the oscillators can spontaneously form two complementary groups. While a group of oscillators rotates coherently, the remaining oscillators perform an erratic motion. This surprising co-existence of synchronous and asynchronous motion in a system of identical oscillators was named chimera state 2 and was subsequently found for a rich variety of different network topologies, oscillator types, and coupling schemes.3,4 So far, most work has focussed on chimera states in isolated networks. Realworld networks, however, are typically not isolated but connected to other networks. It is therefore essential to investigate the interplay of chimera states across separate networks. We here demonstrate that a simple coupling of oscillators across networks allows one to induce different types of synchronization between the networks. In particular, this includes generalized synchronization, where the state of a driving network fully determines the state of a response network, while both networks still show chimera states with distinct...

HighlightsAdaptive generalizations to ISI-distance, SPIKE-distance and SPIKE-synchronization.Generalizations disregard spike time differences not relevant on a more global scale.Rate-independent extension RIA-SPIKE-distance focuses specifically on spike timing.Correction of edge effects and treatment of special cases.