Stochastic Resonance
noise-enhanced signal detection · double-well potential
Double-well potential + signal + particle trajectory
Noisy signal (subthreshold input)
Output (threshold crossings)
SNR vs noise amplitude (stochastic resonance curve)
Signal A
0.70
Signal freq
0.05
Noise σ
0.80
Threshold θ
1.00
Potential a
1.00
Damping γ
0.50
Scan SNR curve
SNR: —
Crossings: —
Coherence: —
Stochastic resonance
: noise can improve signal detection in nonlinear systems.
V(x) = −ax²/2 + x⁴/4 (double well)
Kramers rate: r_K = (a/π)exp(−ΔV/σ²)
Optimal SNR at intermediate noise level — neither too quiet (no switching) nor too loud (random noise dominates).