Single phase-slip junction site can synchronize a parallel superconducting array of linearly coupled Josephson junctions

We study an array of inductively coupled Josephson junctions containing a single phase-slip site in the presence of an alternating current. A phase-slip site with reduced critical current can serve as a permanent source of solitary pulses which can synchronize the dynamics of an infinitely large array of junctions. We find that for definite values of parameters, increasing the coupling constant may prevent this synchronization in a system with periodic boundary conditions. This dependence on the boundary condition can be used as a coding mechanism and the information can be retrieved elsewhere in the array.