MODE-LOCKING, HYSTERESIS AND CHAOS IN COUPLED JOSEPHSON-JUNCTIONS

We study the dynamics of a triangular plaquette of underdamped Josephs on junctions driven by DC's, at zero temperature and in zero magnetic field. We plot the current-voltage characteristics numerically along t hree different directions in the relevant parameter space. In two of t hese cases, the I-V curve contains multiple hysteresis loops, while in the third, the system further displays the period-doubling route to c haos. We try to understand these I-V curves in terms of the phenomenon of mode-locking and of the existence of six special rays, on which th e symmetry of the system forces mathematically constrained solutions. Finally, we interpret several aspects of the system's behaviour in ter ms of vortices.