Optimal noise enhances signal detection in a double-well potential
SNR: — | Phase lag: —
Double-well potential V(x) = −x²/2 + x⁴/4. A subthreshold periodic signal A cos(ωt) plus Gaussian noise ξ(t) drives a particle over the barrier. At optimal noise D*, the system switches synchronously with the signal, maximizing the signal-to-noise ratio (SNR). The SNR curve (right) shows the characteristic bell shape — stochastic resonance.