Synchronization of a Josephson junction array in terms of global variables

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.