The synchronization and signal processing properties of a linearly coupled chain of N overdamped bistable elements, subject to a deterministic periodic signal and uncorrelated white noise, are addressed in the continuum limit of a ${\phi }^4$ field theory. The scaling relations for the optimum noise and coupling strengths that correspond to the observed spatiotemporal stochastic resonance are derived via the ${\phi }^4$ theory and shown to conform to the results of earlier numerical simulations in the large N limit.

• Received 29 September 1995

DOI:https://doi.org/10.1103/PhysRevLett.76.2609