A subthreshold signal (amplitude A < threshold θ) normally cannot trigger a bistable system.
Adding noise of optimal strength causes the noisy signal to cross the threshold in synchrony
with the input — noise helps, not hurts.
Model: double-well potential V(x) = −x²/2 + x⁴/4.
Langevin equation: ẋ = −V'(x) + A·sin(2πft) + ση(t).
SNR is maximized at an optimal intermediate noise level — the hallmark of stochastic resonance.
Observed in sensory neurons, photoreceptors, ion channels, and climate models.