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

We analyze the stochastic response of a finite set of globally coupled noisy bistable units driven by rather weak time-periodic forces. We focus on the stochastic resonance and phase frequency synchronization of the collective variable, defined as the arithmetic mean of the variable characterizing each element of the array. For single unit systems, stochastic resonance can be understood with the powerful tools of linear response theory. Proper noise induced phase frequency synchronization for a single unit system in this linear response regime does not exist. For coupled arrays, our numerical simulations indicate an enhancement of the stochastic resonance effects leading to gains larger than unity as well as genuine phase frequency synchronization. The non-monotonicity of the response with the strength of the coupling strength is investigated. Comparison with simplifying schemes proposed in the literature to describe the random response of the collective variable is carried out.