Stochastic Resonance: Double-Well

Too little noise: particle stays trapped. Too much: random. Just right: noise drives transitions in sync with the weak periodic signal — the SNR peaks.

Noise σ 0.40

Signal amplitude A 0.10

Frequency ω 0.10

ẋ = −V'(x) + A cos(ωt) + σξ(t), V(x) = x⁴/4 − x²/2
Kramer rate: r_K = (1/π)·exp(−ΔV/σ²), ΔV = barrier height. SNR maximized when r_K ≈ ω/2π.