Transition to chaos by interaction of resonances in dissipative systems. II. Josephson junctions, charge-density waves, and standard maps

We have studied the transition to chaos caused by interaction and overlap of resonances in some condensed-matter systems by constructing and analyzing appropriate return maps. In particular, the resistively shunted Josephson junction in microwave fields and charge-density waves in rf electric fields may be described by the differential equation of the damped driven pendulum in a periodic force. The two-dimensional return map for this equation is shown to collapse to a one-dimensional circle map in a parameter regime including the transition to chaos. Phase locking, noise, and hysteresis in these systems can thus be understood in a simple and coherent way by taking over theoretical results for the circle map, some of which were derived in the preceding paper. In order to understand the contraction to one dimensionality we have studied the two-dimensional Chirikov standard map with dissipation. A well-defined transition line along which the system exhibits circle-map critical behavior was found. At this line the system is always phase locked. We conclude that recent theoretical results on universal behavior can readily be checked experimentally by studying systems in condensed-matter physics. The relation between theory and experiment is simple and direct.