Stochastic Resonance
Noise-Enhanced Signal Detection in a Bistable Potential
Parameters
Noise level D:
0.20
Signal amplitude A:
0.10
Signal frequency Ω:
0.050
Well asymmetry ε:
0.00
▶ Start
Statistics
Position x
0.00
Well state
—
Switching rate
0
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)