Stochastic Resonance — Kramers Escape Rate

Double-well potential U(x) = -ax²/2 + bx⁴/4 driven by periodic force + noise

Potential & Particle

Output Signal & SNR

Parameters

Kramers rate r_K ≈
Current well:
Switches: 0
SNR: dB
Stochastic resonance: SNR peaks at an optimal noise level. Kramers rate r_K = (ω_a·ω_b)/(2πγ)·exp(−ΔU/D) where D=σ²/2.

SNR vs Noise (sweep)