  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.
