Synchronization of a Josephson junction array in terms of global variables

TL;DR

This paper models the synchronization behavior of Josephson junction arrays with a common load using global variables, revealing bistability and transition dynamics through analytical and numerical methods.

Contribution

It applies the Watanabe-Strogatz approach to Josephson junction arrays, deriving a finite set of equations for identical junctions and formulating integro-differential equations for disordered arrays.

Findings

Identifies bistability regions of synchronous and asynchronous states.

Analyzes stability of asynchronous states numerically.

Describes transition properties between synchrony and asynchrony.

Abstract

We consider an array of Josephson junctions with a common LCR-load. Application of the Watanabe-Strogatz approach [Physica D, v. 74, p. 197 (1994)] allows us to formulate the dynamics of the array via the global variables only. For identical junctions this is a finite set of equations, analysis of which reveals the regions of bistability of the synchronous and asynchronous states. For disordered arrays with distributed parameters of the junctions, the problem is formulated as an integro-differential equation for the global variables, here stability of the asynchronous states and the properties of the transition synchrony-asynchrony are established numerically.