Scaling laws for spatiotemporal synchronization and array enhanced stochastic resonance

Recently, the synchronization and signal processing ability of a locally and linearly coupled array of bistable elements was enhanced by the addition of uncorrelated noise [J. F. Lindner, B. K. Meadows, W. L. Ditto, M. E. Inchiosa, and A, R. Bulsara, Phys. Rev. Lett. 75, 3 (1995)]. Here, we detail the performance of such an array as a function of both coupling and noise. Simple theoretical arguments, grounded in extensive numerical studies, suggest how to ''tune'' the array for best synchronization and signal-to-noise ratio. Specifically, we propose that, for large array size N, the optimal coupling scales like N-2 and the optimal noise variance scales like N. This scaling matches the coupling-induced correlation length to the array length and the noise-generated mean hopping time to the modulation period, thereby creating a stochastic resonance in space and time.