Chimera states in multiplex networks: Chameleon-like across-layer synchronization

Different across-layer synchronization types of chimera states in multilayer networks have been discovered recently. We investigate possible relations between them, for example, if the onset of some synchronization type implies the onset of some other type. For this purpose, we use a two-layer network with multiplex inter-layer coupling. Each layer consists of a ring of non-locally coupled phase oscillators. While oscillators in each layer are identical, the layers are made non-identical by introducing mismatches in the oscillators' mean frequencies and phase lag parameters of the intra-layer coupling. We use different metrics to quantify the degree of various across-layer synchronization types. These include phase-locking between individual interacting oscillators, amplitude and phase synchronization between the order parameters of each layer, generalized synchronization between the driver and response layer, and the alignment of the incoherent oscillator groups' position on the two rings. For positive phase lag parameter mismatches, we get a cascaded onset of synchronization upon a gradual increase of the inter-layer coupling strength. For example, the two order parameters show phase synchronization before any of the interacting oscillator pairs does. For negative mismatches, most synchronization types have their onset in a narrow range of the coupling strength. Weaker couplings can destabilize chimera states in the response layer toward an almost fully coherent or fully incoherent motion. Finally, in the absence of a phase lag mismatch, sufficient coupling turns the response dynamics into a replica of the driver dynamics with the phases of all oscillators shifted by a constant lag.

Automated summary

Different synchronization types of chimera states have been discovered in multilayer networks. This study investigates the possible relationships between these synchronization types, specifically if the onset of one type implies the onset of another. Using a two-layer network with non-locally coupled phase oscillators, the researchers introduced mismatches in mean frequencies and phase lag parameters to make the layers non-identical. Various metrics were used to measure the degree of synchronization, including phase-locking, amplitude and phase synchronization between order parameters, generalized synchronization, and alignment of incoherent oscillator groups. Positive phase lag parameter mismatches resulted in a cascaded onset of synchronization, while negative mismatches led to most synchronization types occurring within a narrow range of coupling strength. Weaker couplings could destabilize chimera states in the response layer, and in the absence of a phase lag mismatch, sufficient coupling caused the response dynamics to replicate the driver dynamics with a constant phase lag.