Stochastic Resonance

Noise-Enhanced Signal Detection in a Bistable Potential

Parameters

Statistics

Position x0.00
Well state
Switching rate0
SNR (est.)
Kramers rate r_K

Theory

dx/dt = −dU/dx + A·cos(Ωt) + ξ(t)

U(x) = −x²/2 + x⁴/4 + ε·x
Minima at x ≈ ±1

Kramers rate:
r_K = (1/2π)·exp(−ΔU/D)

Optimal noise: D* ≈ ΔU / ln(Ω/2π r_K)