Flux bias-controlled chaos and extreme multistability in SQUID oscillators

TL;DR

This paper investigates the complex dynamical behaviors of rf SQUID oscillators, revealing multistability, chaos, and bifurcations in strongly nonlinear regimes, with potential for controlled state switching.

Contribution

It provides a detailed analysis of multistability and chaos in SQUIDs using a realistic model, highlighting new bifurcation structures and control mechanisms.

Findings

Extreme multistability near resonance frequencies

Chaotic regions in parameter space

State switching between chaos and periodicity

Abstract

The radio frequency (rf) Superconducting QUantum Interference Device (SQUID) is a highly nonlinear oscillator exhibiting rich dynamical behavior. It has been studied for many years and it has found numerous applications in magnetic field sensors, in biomagnetism, in non-destructive evaluation, and gradiometers, among others. Despite its theoretical and practical importance, there is relatively very little work on its multistability, chaotic properties, and bifurcation structure. In the present work, the dynamical properties of the SQUID in the strongly nonlinear regime are demonstrated using a well-established model whose parameters lie in the experimentally accessible range of values. When driven by a time-periodic (ac) flux either with or without a constant (dc) bias, the SQUID exhibits extreme multistability at frequencies around the (geometric) resonance. This effect is manifested by a "snake-like" form of the resonance curve. In the presence of both ac and dc flux, multiple bifurcation sequences and secondary resonance branches appear at frequencies above and below the geometric resonance. In the latter case, the SQUID exhibits chaotic behavior in large regions of the parameter space; it is also found that the state of the SQUID can be switched from chaotic to periodic or vice versa by a slight variation of the dc flux.