Stochastic Resonance

Noise can enhance weak signal detection — optimal noise maximizes SNR

Signal amplitude A0.70

Signal frequency f0.50

Noise level σ0.80

Barrier height ΔV1.20

ẋ = −V'(x) + A·cos(2πft) + σ·ξ(t) | V(x) = −x²/2 + x⁴/4 | Kramer rate: r_K = exp(−ΔV/σ²)

SNR = 0.00 dB | Crossings = 0 | Optimal σ ≈ 0.87

In a bistable potential driven by a weak subthreshold signal, adding the right amount of noise enables threshold crossings synchronized with the signal — stochastic resonance. The SNR vs noise curve has a peak at the optimal noise level. Found in neurons, sensory systems, and climate models.