Mode-locking, hysteresis and chaos in coupled Josephson junctions

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Abstract

We study dynamics of a triangular plaquette of underdamped Josephson junctions driven by DC's, at Zero temperature and in zero magnetic field. We plot the current-voltage characteristics numerically along three different directions in the relevant parameter space. In two of these, the I–V curve contains multiple hysteresis loops, while in the third, the system further displays the period-doubling route to chaos. 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 the symmetry of the system forces mathematically constrained solutions. Finally, we interpret several aspects of the system's behaviour in terms of vortices.

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