Phase Shifts in Stochastic Resonance

The response of an overdamped bistable system to a weak periodic force in the presence of external noise is investigated using linear-response theory and by analog electronic experiment. It is shown, both theoretically and experimentally, that a phase lag $\phi$ exists between the force and the response, and that $\left|\phi \right|$ passes through a maximum when the noise intensity is tuned through the range where stochastic resonance occurs. These results clarify the interrelation between stochastic resonance and conventional resonance phenomena, and confirm that stochastic resonance can usefully be treated by linear-response theory.