Mutual locking, chaos and devils staircase in two Josephson tunnel junctions with a common resistive shunt

The authors studied the phase-locking in a pair of individually biased, resistively and capacitively shunted Josephson junctions, coupled by a common resistive or capacitive shunt, on an analog computer. Under certain conditions, locking is found to occur at all rational frequency ratios. A critical line is found in parameter space along which the steps form a complete devil's staircase having a fractal dimension of 0.87. Beyond the critical line bifurcations occur on all steps following the Feigenbaum sequence to chaos. The Feigenbaum constants are recovered to a fair accuracy. Preliminary experiments with two Josephson tunnel junctions shunted on the chip by a gold-indium film are discussed.<
>