Stochastic Resonance — Optimal Noise Level

A subthreshold signal becomes detectable only with the right amount of noise. SNR peaks at an optimal noise level — too little or too much and the signal is lost.

Threshold θ = 1.0
Current SNR
SNR = 0.00 dB
Crossings: —
Stochastic resonance (Benzi 1981, Gammaitoni 1998): noise-assisted signal detection. The bistable potential V(x)=−x²/2+x⁴/4 has wells separated by a barrier. Noise induces Kramers transitions; at optimal σ these sync with the signal.

Found in: neuroscience (neural firing), sensory systems (hair cells, mechanoreceptors), electronics, climate models (glacial cycles).