LAUSR

Abstract We consider the classical double-well model of stochastic resonance, in which a particle in a potential V ( x , t ) = [ − x 2 ∕ 2 + x 4 ∕ 4 − A sin ( ω t ) x ] is subject to an additional stochastic forcing that causes it to occasionally jump between the two wells at x ≈ ± 1 . We present direct numerical solutions of the Fokker–Planck equation for the probability density function p ( x , t ) , for ω = 1 0 − 2 to 1 0 − 6 , and A ∈ [ 0 , 0 . 2 ] . Previous results that stochastic resonance arises if ω matches the average frequency at which the stochastic forcing alone would cause the particle to jump between the wells are quantified. The modulation amplitudes A necessary to achieve essentially 100% saturation of the resonance tend to zero as ω → 0 . From p ( x , t ) we next construct the information length L ( t ) = ∫ [ ∫ ( ∂ t p ) 2 ∕ p d x ] 1 ∕ 2 d t , measuring changes in information associated with changes in p . L shows an equally clear signal of the resonance, which can be interpreted in terms of the underlying meaning of L . Finally, we present escape time calculations, where the Fokker–Planck equation is solved only for x ≥ 0 , and find that resonance shows up less clearly than in either the original p or L .