Stochastic resonance: Linear response and giant nonlinearity

Abstract

The response of a bistable noise-driven system to a weak periodic force is investigated using linear response theory (LRT) and by analogue electronic experiment. For quasithermal systems the response, and in particular its increase with increasing noise intensityD, are described by the fluctuationdissipation relations. For smallD the low-frequency susceptibility of the systemχ(ω) has been found in explicit form allowing for both forced oscillations about the states and periodic modulation of the probabilities of fluctuational transitions between the states. It is shown, both theoretically and experimentally, that a phase lagφ between the force and the response passes through a maximum whenD is tuned through the range where stochastic resonance (SR) occurs. A giant nonlinearity of the response is shown to arise for smallD and small frequencies of the driving force. It results in the signal induced by a sinusoidal force being nearly rectangular. The range of applicability of LRT is established.