# Pattern formation and chimera states in 2D SQUID metamaterials

## TL;DR

This paper explores complex pattern formation, including Turing-like and chimera states, in two-dimensional SQUID metamaterials driven by periodic magnetic flux, revealing rich dynamical behaviors and controllability of these patterns.

## Contribution

It demonstrates the emergence and control of Turing-like and chimera patterns in 2D SQUID metamaterials, highlighting their coexistence and bifurcation scenarios.

## Key findings

- Turing-like patterns occur near the synchronization transition.
- Chimeras emerge from multistability near geometric resonance.
- Patterns can be controlled by varying system parameters.

## 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.