Vulnerability to Noise of A Phase-Locked Oscillator Array

The effect of noise on the in-phase of a set of $N$ globally coupled oscillators is studied; these discrete-time maps are associated with the continuous-time equations of motion for a series array of Josephson junction oscillators. We investigate both geometrical properties of the basin of attration in the large $N$ limit, and the implications of this geometry on the average time for the system to escape from the phase-kicked mode. Our main results are that the attractor basin maintains a box-shaped ``core'' of finite radius even as $N\rightarrow\infty$, and that the in-phase attractor if a large $N$ array is much less vulnerable to noise than are the out-of-phase attractors.