论文标题
超导二聚体中的多分支共振，通过准碘的混乱和不对称状态
Multi-branched resonances, chaos through quasiperiodicity, and asymmetric states in a superconducting dimer
论文作者
论文摘要
相互对称性耦合的两个相同的鱿鱼（超导量子干扰装置）的系统通过其相互感应并由正弦场驱动，相对于动态特性，例如其乘坐的谐振曲线，其分叉结构，以及其同步行为。发现该鱿鱼二聚体表现出滞后共振曲线，并通过Neimark-Sacker（torus）分叉连接起来，并在其附近共存混乱的分支。有趣的是，鱿鱼二聚体向混乱的过渡是通过二维圆环（quasiperiodicitionto to-chaos transition）的级数加倍的级联而发生的。通过计算出的Lyapunov光谱鉴定了混沌态，并确定了它们的吸引力盆地。分叉图已在耦合强度的参数平面和应用场的驱动频率上构造，并将其超级置于同一平面上最大Lyapunov指数的地图上。通过这种方式，揭示了混乱行为与圆环分叉之间的明确联系。此外，已经使用螺纹螺纹乌贼环之间的相关函数检测到类似于局部同步的不对称状态。似乎在鱿鱼二聚体中存在的间歇性混沌同步的影响仅略微接触。
A system of two identical SQUIDs (superconducting quantum interference devices) symmetrically coupled through their mutual inductance and driven by a sinusoidal field is investigated numerically with respect to dynamical properties such as its multibranched resonance curve, its bifurcation structure, as well as its synchronization behavior. The SQUID dimer is found to exhibit a hysteretic resonance curve with a bubble connected to it through Neimark-Sacker (torus) bifurcations, along with coexisting chaotic branches in their vicinity. Interestingly, the transition of the SQUID dimer to chaos occurs through a period-doubling cascade of a two-dimensional torus (quasiperiodicity-to-chaos transition). The chaotic states are identified through the calculated Lyapunov spectrum, and their basins of attraction have been determined. Bifurcation diagrams have been constructed on the parameter plane of the coupling strength and the driving frequency of the applied field, and they are superposed to maps of the maximum Lyapunov exponent on the same plane. In this way, a clear connection between chaotic behavior and torus bifurcations is revealed. Moreover, asymmetric states that resemble localized synchronization have been detected using the correlation function between the fluxes threading the loop of the SQUIDs. The effect of intermittent chaotic synchronization, which seems to be present in the SQUID dimer, is only slightly touched.
