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We analyze the stochastic response of a finite set of globally coupled noisybistable units driven by rather weak time-periodic forces. We focus on thestochastic resonance and phase frequency synchronization of the collectivevariable, defined as the arithmetic mean of the variable characterizing eachelement of the array. For single unit systems, stochastic resonance can beunderstood with the powerful tools of linear response theory. Proper noiseinduced phase frequency synchronization for a single unit system in this linearresponse regime does not exist. For coupled arrays, our numerical simulationsindicate an enhancement of the stochastic resonance effects leading to gainslarger than unity as well as genuine phase frequency synchronization. Thenon-monotonicity of the response with the strength of the coupling strength isinvestigated. Comparison with simplifying schemes proposed in the literature todescribe the random response of the collective variable is carried out.

The role of fluctuations in the response of coupled bistable units to weak driving time-periodic forces