Oscillatory Regimes in a 1D Josephson Junction Array with a Nonlocal Delayed Coupling

Abstract

We have numerically investigated a series array of electromagnetically coupled Josephson junctions considering the coupling delay. In the general case of a nonzero delay, we have derived equations for the slow and fast phases in the low-frequency approximation. We have studied the regimes of oscillations of a Josephson junction array for different positions of the bias point on the current–voltage characteristics (including its reverse branch). Similar analysis has been performed for systems of equations without coupling delay and for an arbitrary bias current. Several regimes of steady-state oscillations have been detected, i.e. synchronous oscillations, traveling wave regime, regime of partial switching-off of junctions, and chimera states.