Abstract
The interaction of nonrelativistic (anti-) fluxons in two coupled-ring Josephson junctions under the action of external currents is considered by using adiabatic perturbation theory. The asymptotic static and dynamic states and conditions for their coexistence are found from qualitative analysis of the system in the phase space. These states correspond to separate stable branches in the current-voltage characteristics, so that hysteresis occurs in a system. Comparison with numerical calculations shows a qualitative agreement with analytical predictions.
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