Synchronization transitions in a hyperchaotic SQUID Trimer

TL;DR

This paper investigates synchronization phenomena in a hyperchaotic SQUID trimer, revealing transitions between complete and intermittent chaos synchronization using numerical analysis and Lyapunov spectra.

Contribution

It provides the first detailed numerical analysis of synchronization transitions in a hyperchaotic SQUID trimer with realistic parameters.

Findings

Identified complete chaos synchronization between SQUIDs.

Observed intermittent chaos synchronization.

Linked synchronization transitions to chaos-hyperchaos transitions.

Abstract

The phenomena of intermittent and complete synchronization between two out of three identical, magnetically coupled SQUIDs (Superconducting QUantum Interference Devices) are investigated numerically. SQUIDs are highly nonlinear superconducting oscillators/devices that exhibit strong resonant and tunable response to applied magnetic field(s). Single SQUIDs and SQUID arrays are technologically important solid state devices, and they also serve as a testbed for exploring numerous complex dynamical phenomena. In SQUID oligomers, the dynamic complexity increases considerably with the number of SQUIDs. The SQUID trimer, considered here in a linear geometrical configuration using a realistic model with accesible control parameters, exhibits chaotic and hyperchaotic behavior in wide parameter regions. Complete chaos synchronization as well as intermittent chaos synchronization between two SQUIDs of the trimer is identified and characterized using the complete Lyapunov spectrum of the system and appropriate measures. The passage from complete to intermittent synchronization seems to be related to chaos-hyperchaos transitions as has been conjectured in the early days of chaos synchronization.