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

Area of Science:

• Complex networks
• Nonlinear dynamics
• Statistical physics

Background:

• Chimera states, a phenomenon where coexisting coherent and incoherent behaviors emerge in identical elements, have been observed in multilayer networks.
• Recent studies have identified various types of across-layer synchronization in these networks.

Purpose of the Study:

• To investigate the relationships between different across-layer synchronization types in multilayer networks.
• To determine if the onset of one synchronization type implies the onset of another.

Main Methods:

• A two-layer network with multiplex inter-layer coupling was constructed.
• Each layer comprised non-locally coupled phase oscillators, with layers made non-identical by frequency and phase lag mismatches.
• Metrics including phase-locking, order parameter synchronization, generalized synchronization, and incoherent group alignment were used to quantify synchronization.

Main Results:

• Positive phase lag mismatches resulted in a cascaded onset of synchronization with increasing inter-layer coupling.
• Order parameter phase synchronization preceded individual oscillator synchronization for positive mismatches.
• Negative mismatches led to a narrow coupling strength range for the onset of most synchronization types.
• Weaker couplings could destabilize chimera states in the response layer.
• Absence of phase lag mismatch and sufficient coupling led to replica dynamics in the response layer.

Conclusions:

• The interplay between layer non-identities and inter-layer coupling strength dictates the emergence and sequence of across-layer synchronization types.
• Understanding these relationships is crucial for controlling and predicting complex dynamics in multilayer systems.