Physical properties of transition to chaos in RF-driven Josephson junction analog

An analog circuit is used to investigate the behavior of the transition to chaos in the rf-driven Josephson junction under the variation of excitation amplitude and frequency with McCumber parameter >1. A series of transitions is observed, including a hysteretic jump, symmetry breaking, period doubling, and intermittency prior to chaos, and the transition boundaries are given in a state diagram in the vs. parameter space. Thus, the sequence of transitions to chaos can be inferred from this diagram. Based on these results, the harmonic balance method and Floquet theory are applied to study the instability of the transition series. It is suggested that all these transitions to chaos can be explained as parametric excitations. In addition, the transition boundaries in the state diagram can be satisfactorily computed from the conditions with a Floquet multiplier =±1.