dx/dt = x − x³ + A·sin(ωt) + σ·η(t). The double-well potential V(x) = −x²/2 + x⁴/4 has two minima at x=±1. A weak periodic signal (below the threshold to cross) normally can't drive transitions. Adding optimal noise triggers noise-assisted hopping synchronized with the signal — the Signal-to-Noise Ratio peaks at an optimal noise level σ*. This is stochastic resonance: noise improves signal detection.