Nonlinear stochastic resonance: the saga of anomalous output-input gain

We reconsider stochastic resonance (SR) for an overdamped bistable dynamics driven by a harmonic force and Gaussian noise from the viewpoint of the gain behavior, i.e., the signal-to-noise ratio (SNR) at the output divided by that at the input. The primary issue addressed in this work is whether a gain exceeding unity can occur for this archetypal SR model, for subthreshold signals that are beyond the regime of validity of linear response theory: in contrast to nondynamical threshold systems, we find that the nonlinear gain in this conventional SR system exceeds unity only for suprathreshold signals, where SR for the spectral amplification and/or the SNR no longer occurs. Moreover, the gain assumes, at weak to moderate noise strengths, rather small (minimal) values for near-threshold signal amplitudes. The SNR gain generically exhibits a distinctive nonmonotonic behavior versus both the signal amplitude at fixed noise intensity and the noise intensity at fixed signal amplitude. We also test the validity of linear response theory; this approximation is strongly violated for weak noise. At strong noise, however, its validity regime extends well into the large driving regime above threshold. The prominent role of physically realistic noise color is studied for exponentially correlated Gaussian noise of constant intensity scaling and also for constant variance scaling; the latter produces a characteristic, resonancelike gain behavior. The gain for this typical SR setup is further contrasted with the gain behavior for a "soft" potential model.