Pattern formation and chimera states in 2D SQUID metamaterials
arXiv:1908.00004 · doi:10.1063/1.5122307
Abstract
The Superconducting QUantum Interference Device (SQUID) is a highly nonlinear oscillator with rich dynamical behavior, including chaos. When driven by a time-periodic magnetic flux, the SQUID exhibits extreme multistability at frequencies around the geometric resonance which is manifested by a "snake-like" form of the resonance curve. Repeating motifs of SQUIDs form metamaterials, i. e. artificially structured media of weakly coupled discrete elements that exhibit extraordinary properties, e. g. negative diamagnetic permeability. We report on the emergent collective dynamics in two-dimensional lattices of coupled SQUID oscillators, which involves a rich menagerie of spatio-temporal dynamics, including Turing-like patterns and chimera states. Using Fourier analysis we characterize these patterns and identify characteristic spatial and temporal periods. In the low coupling limit, the Turing-like patterns occur near the synchronization-desynchronization transition which can be related to the bifurcation scenarios of the single SQUID. Chimeras emerge due to the multistability near the geometric resonance, and by varying the dc component of the external force we can make them appear and reappear and, also, control their location. A detailed analysis of the parameter space reveals the coexistence of Turing-like patterns and chimera states in our model, as well as the ability to transform between these states by varying the system parameters.
References in corpus (28)
- Chimera States for Coupled Oscillators
- Chimera states: Coexistence of coherence and incoherence in networks of coupled oscillators
- Coexistence of Coherence and Incoherence in Nonlocally Coupled Phase Oscillators
- A classification scheme for chimera states
- Spatiotemporal complexity of a ratio-dependent predator-prey system
- Progress in Superconducting Metamaterials
- Towards Realizing a Quantum Memory for a Superconducting Qubit: Storage and Retrieval of quantum states
- Chimera patterns in two-dimensional networks of coupled neurons
- rf SQUID metamaterials
- Chimeras in SQUID Metamaterials
- Robust chimera states in SQUID metamaterials with local interactions
- A multi-stable switchable metamaterial
- A one-dimensional tunable magnetic metamaterial
- Realization and modeling of rf superconducting quantum interference device metamaterials
- Networks of coupled oscillators: from phase to amplitude chimeras
- Three-dimensional chimera patterns in networks of spiking neuron oscillators
- Tunable Broadband Transparency of Macroscopic Quantum Superconducting Metamaterials
- Multistability and Self-Organization in Disordered SQUID Metamaterials
- Flux bias-controlled chaos and extreme multistability in SQUID oscillators
- Coherent Oscillations of Driven rf SQUID Metamaterials
- Chimera states and synchronization in magnetically driven SQUID metamaterials
- Intermodulation in Nonlinear SQUID Metamaterials: Experiment and Theory
- Two-tone spectroscopy of a SQUID metamaterial in the nonlinear regime
- Dissipative discrete breathers in rf SQUID metamaterials
- Transient Chaos Generates Small Chimeras
- Imaging collective behavior in an rf-SQUID metamaterial tuned by DC and RF magnetic fields
- Controlled Generation of Chimera States in SQUID Metasurfaces using DC Flux Gradients
- Multistable Dissipative Breathers and Novel Collective States in SQUID Lieb Metamaterials
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- Identification of Chimera using Machine Learning
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- Tuning of Strong Nonlinearity in rf SQUID Meta-Atoms
- Stripes on finite domains: Why the zigzag instability is only a partial story
- Effects of Strong Capacitive Coupling Between Meta-Atoms in rf SQUID Metamaterials
- Chimera states in ring-star network of Chua circuits