Bulk-SQUID effect in a discrete superconductor as a consequence of generation frequency locking in constituent josephson junctions

The theory of the bulk-SQUID effect in discrete superconductors is constructed for the first time. It is shown that the bulk-SQUID effect emerges in the system of 2D intrinsically stochastic multijunction SQUID (i.e., with random values of critical currents of the junctions, injection currents, and the coupling coefficients between the junction) due to generation frequency locking in all junctions. It is demonstrated that the bulk-SQUID effect occurs in a wide range of random parameters of the system. This domain of variation of the system parameters can be divided into three subdomains. The first one is the subdomain of coherent dynamics of phases at the junctions, the second is the subdomain of incoherent dynamics, in which the phases of the junctions are not locked, but the bulk-SQUID effect persists, and the third is the subdomain of transient dynamics, in which coherent dynamics and the bulk-SQUID effect are observed in parts. A simple mathematical model of noninteracting junctions, which correctly describes basic features of the dynamics of the initial system and makes it possible to calculate some of its statistical characteristics, is proposed and analyzed.