Phase locking dynamics in 2D Josephson junction arrays with small inductances

Phase locking in a basic two-dimensional hybrid Josephson junction array consisting of two rows and four columns is investigated exploiting the small inductance approximation. The general synchronization dynamics agrees with that of simpler systems. Especially, the junction voltages within the same row oscillate practically in phase unless the external magnetic flux in the loops is near to multiples of a quarter of the flux quantum. In case of a finite flux we have found a stable antiphase regime of both uniform interferometer oscillations whereas in the zero-field limit this locking regime is neutrally stable.