Abstract:
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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. |
Abstract:
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We acknowledge funding from the Volkswagen foundation, the Spanish Ministry of Economy and
Competitiveness, Grant No. FIS2014-54177-R, the CERCA Programme of the Generalitat de Catalunya (R.G.A. and G.R.), and from the European Union’s Horizon 2020 research and innovation programme under the Marie
Sklodowska-Curie Grant Agreement No. 642563 (R.G.A. and I.M.). |