Noise can enhance detection of weak subthreshold signals
Parameters
Signal-to-Noise Ratio (SNR)
—
dx = (-x³/3 + x + A·sin(ωt))dt + σ·dW
In a bistable system, a subthreshold signal (A < θ) alone can't trigger crossings. Adding the right amount of noise enables resonant threshold crossings synchronized to the signal.
SNR peaks at optimal σ — too little noise: no crossings; too much: random. The phenomenon appears in neuroscience, sensory biology, and signal processing.