Hizanidis J, Lazarides N, Tsironis G P
Department of Physics, University of Crete, P. O. Box 2208, 71003 Heraklion, Greece and National University of Science and Technology MISiS, Leninsky Prospekt 4, Moscow 119049, Russia.
Chaos. 2018 Jun;28(6):063117. doi: 10.1063/1.5020949.
The radio frequency (rf) Superconducting QUantum Interference Device (SQUID) is a highly nonlinear oscillator exhibiting the 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.
射频（rf）超导量子干涉器件（SQUID）是一种高度非线性振荡器，展现出丰富的动力学行为。它已被研究多年，并在磁场传感器、生物磁学、无损检测以及梯度仪等众多领域得到了广泛应用。尽管其在理论和实践方面都具有重要意义，但关于其多稳定性、混沌特性和分岔结构的研究相对较少。在本研究中，我们使用一个成熟的模型来展示SQUID在强非线性区域的动力学特性，该模型的参数处于实验可获取的值范围内。当由具有或不具有恒定（直流）偏置的时间周期（交流）磁通驱动时，SQUID在（几何）共振频率附近表现出极端的多稳定性。这种效应通过共振曲线的“蛇形”形式体现出来。在同时存在交流和直流磁通的情况下，在几何共振频率之上和之下的频率处会出现多个分岔序列和次级共振分支。在后一种情况下，SQUID在参数空间的很大区域内表现出混沌行为；还发现通过略微改变直流磁通，SQUID的状态可以从混沌切换到周期状态，反之亦然。
