Stochastic resonance: theory and numerics

We address the phenomenon of stochastic resonance in a noisy bistable system driven by a time-dependent periodic force (not necessarily sinusoidal) and in its two-state approximation. Even for driving forces with subthreshold amplitudes, the behavior of the system response might require a nonlinear description. We introduce analytical and numerical tools to analyze the power spectral amplification and the signal-to-noise ratio in a nonlinear regime. Our analysis shows the importance of the effects of the driving force on the system fluctuations in a nonlinear regime. These effects can be usefully exploited to achieve high quality output signals with gains larger than unity, which is impossible within a linear regime.