Stochastic resonance in a mean-field model of cooperative behavior

We study the long-time response of a stochastic system formed by very many interacting subsystems coupled by a mean-field interaction and subject to a time periodic external field. In the absence of a driving field; the system shows an order-disorder phase transition and its time evolution is well described by a Fokker-Planck equation which is nonlinear in the probability density. We carry out an analysis of the dynamics in the case of a weak driving field by means of a perturbation analysis (linear response theory). The response of the system is then given in terms of a generalized susceptibility. Its evaluation shows that the phenomenon of stochastic resonance, typical of driven bistable systems, is greatly enhanced by the dynamical feedback induced by mean-field coupling.