Phase synchronization in an array of driven Josephson junctions

TL;DR

This paper investigates how Josephson junction arrays can achieve phase and chaotic synchronization under external biasing, revealing conditions for synchronization stability and the effects of phase differences on system dynamics.

Contribution

It introduces new insights into synchronization conditions in Josephson junction arrays, including stability analysis and the impact of phase differences on chaotic and periodic behavior.

Findings

Outer junctions can synchronize independently of inner ones.

Phase differences induce phase synchronization across all junctions.

Chaotic motion transitions to periodic with phase differences.

Abstract

We consider an array of N Josephson junctions connected in parallel and explore the condition for chaotic synchronization. It is found that the outer junctions can be synchronized while they remain uncorrelated to the inner ones when an external biasing is applied. The stability of the solution is found out for the outer junctions in the synchronization manifold. Symmetry considerations lead to a situation wherein the inner junctions can synchronize for certain values of parameter. In the presence of a phase difference between the applied fields, all the junctions exhibit phase synchronization. It is also found that chaotic motion changes to periodic in the presence of phase differences.