Stochastic resonance in the strong-forcing limit

Asymmetric bistable systems subject to periodic and stochastic forcing in the strongly nonlinear regime: the power spectrum

In this, the fourth of a series of papers [the first three papers were Phys. Rev. E 68, 016103 (2003), 68, 036133 (2003), and Phys. Lett. A 334, 12 (2005)] on the response of overdamped noisy bistable systems subject to an asymmetrizing constant signal superimposed on a time-sinusoidal driving signal, we obtain analytic expressions for the power spectral density of the response, including a detailed theoretical analysis of the power spectrum. The results are valid for any two-state system, however the specific case of the Duffing (or standard quartic) potential is considered in detail. The stochastic dynamics are confined to the weak noise limit (periodic signal amplitude much greater than noise intensity), i.e., when the response of the system to the external periodic field is strongly nonlinear.

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.