# Chimera states in networks of locally and non-locally coupled SQUIDs

## TL;DR

This paper demonstrates the emergence and control of chimera states in SQUID metamaterials, revealing how local and non-local magnetic couplings lead to complex spatial patterns driven by multistability and attractor crowding.

## Contribution

It introduces the first numerical demonstration of chimera states in SQUID metamaterials with both local and non-local couplings, and discusses their control via magnetic flux gradients.

## Key findings

- Chimera states can be generated in SQUID metamaterials under specific initial conditions.
- Both local and non-local couplings support the formation of spatially non-uniform states.
- Control of chimera states is possible using a constant flux gradient.

## Abstract

Planar and linear arrays of SQUIDs (superconducting quantum interference devices), operate as nonlinear magnetic metamaterials in microwaves. Such {\em SQUID metamaterials} are paradigmatic systems that serve as a test-bed for simulating several nonlinear dynamics phenomena. SQUIDs are highly nonlinear oscillators which are coupled together through magnetic dipole-dipole forces due to their mutual inductance; that coupling falls-off approximately as the inverse cube of their distance, i.~e., it is non-local. However, it can be approximated by a local (nearest-neighbor) coupling which in many cases suffices for capturing the essentials of the dynamics of SQUID metamaterials. For either type of coupling, it is numerically demonstrated that chimera states as well as other spatially non-uniform states can be generated in SQUID metamaterials under time-dependent applied magnetic flux for appropriately chosen initial conditions. The mechanism for the emergence of these states is discussed in terms of the multistability property of the individual SQUIDs around their resonance frequency and the attractor crowding effect in systems of coupled nonlinear oscillators. Interestingly, generation and control of chimera states in SQUID metamaterials can be achieved in the presence of a constant (dc) flux gradient with the SQUID metamaterial initially at rest.