Exact formula for power amplification of rectangular periodic signal by nonlinear system with symmetric potential in fully adiabatic limit

The overdamped Brownian diffusion in a symmetric potential with the external rectangular periodic signal is explored. In the fully adiabatic limit when all characteristic times of unperturbed system are much smaller than the period of driven force, the exact quadrature formula to calculate the signal power amplification in nonlinear dynamical system is obtained. Specifically, this relation is analyzed for the piece-wise linear bistable potential in the form of inverted symbol “M”. To find the conditions of applicability of the fully adiabatic limit for investigations of the stochastic resonance phenomenon we compare the results obtained with the results of linear response theory.