Stochastic resonance in a bistable piecewise potential: Analytical solution

We consider a bistable piecewise potential subject to both a periodic signal and a random force. The output signal-to-noise ratio (SNR) is calculated for a small-amplitude periodic signal of arbitrary frequency Omega and noise strength D. Our analysis not only recovers the well known non-monotonic dependence of SNR on D at fixed Omega, but also predicts the non-monotonic dependence of SNR on Omega at fixed D. The latter phenomenon does not appear in the commonly assumed adiabatic approximation which applies only at low frequencies.