Pattern formation and chimera states in 2D SQUID metamaterials.

Area of Science:

• Nonlinear dynamics
• Metamaterials science
• Condensed matter physics

Background:

• Superconducting QUantum Interference Devices (SQUIDs) are nonlinear oscillators exhibiting chaotic dynamics.
• Coupled SQUIDs form metamaterials with unique electromagnetic properties, like negative diamagnetic permeability.

Purpose of the Study:

• Investigate emergent collective dynamics in 2D lattices of coupled SQUID oscillators.
• Characterize spatiotemporal patterns, including Turing-like patterns and chimera states.
• Analyze parameter dependencies and control mechanisms for these complex states.

Main Methods:

• Utilized Fourier analysis to characterize spatiotemporal patterns.
• Studied SQUID lattices driven by time-periodic magnetic flux.
• Analyzed parameter space to identify transitions and coexistence of states.

Main Results:

• Observed Turing-like patterns near synchronization-desynchronization transitions in the low coupling limit.
• Identified chimera states arising from multistability near geometric resonance.
• Demonstrated control over chimera appearance, reappearance, and location by varying external force.
• Revealed coexistence and interconversion of Turing-like patterns and chimera states within the parameter space.

Conclusions:

• Coupled SQUID systems display rich emergent spatiotemporal dynamics.
• Turing-like patterns and chimera states are controllable phenomena in these systems.
• Understanding these dynamics is crucial for developing advanced metamaterials and understanding complex nonlinear systems.