Stochastic resonance of collective variables in finite sets of interacting identical subsystems

We explore stochastic resonance effects in the response of a complex stochastic system formed by a finite number of interacting, identical subunits driven by a time-periodic force. The driving force alone cannot induce sustained oscillations between the different attractors of the dynamics in the absence of noise. We focus on a global stochastic variable defined as the arithmetic mean of the relevant stochastic variable of each subunit. We construct numerical approximations to its first two long time cumulant moments and its long time correlation function. We also compute the output signal-to-noise ratio and the stochastic resonance gain, for a wide range of parameter values and several types of driving forces. The coupling between the subsystems leads, within adequate ranges of the parameter values, to global outputs with very large signal-to-noise ratios. We have also observed gains larger than unity in the global response to subthreshold sinusoidal driving forces.