Unified signal response for stochastic resonance in bistable systems

Stochastic resonance, wherein the stimulus–response of a system can be maximally improved by an intermediate level of noise, has been extensively verified in coupled dynamical systems immersed in colored noisy environments. As yet the roles of noise color, coupling, damping, and the external driving frequency on the signal response remain largely unclear. Here, based on linear response theory, we comprehensively investigate the signal response of systems ranging from a single overdamped bistable oscillator perturbed by Gaussian white noise to the mean-field coupled underdamped Duffing elements disturbed by Ornstein–Uhlenbeck noise. We find that the signal response expressions in these different conditions can be summarized into a uniform Lorentz function form. Furthermore, based on the general formula, we explain explicitly the roles of driving frequency, coupling, and noise color on stochastic resonance. Since bistable systems have served as a testbed to utilize weak signals in energy harvesting devices and colloidal particles, our results thus have theoretical guidance significance on the manipulation of weak signals in realistic fields.