A dynamical phenomenon in which the presence of random fluctuations (noise) in a nonlinear, thresholded system increases the system's coherent response to a weak periodic or subthreshold input, producing an optimal noise intensity that maximizes signal detectability or output periodicity.

Principle

Noise-induced transitions or fluctuations synchronize with an external timescale when the noise-driven transition rate is commensurate with the input period, enhancing the signal-to-noise ratio of the system's response.

Demonstration

A particle in a bistable potential subject to a subthreshold sinusoidal forcing and additive white noise exhibits maximal periodic switching between wells at an intermediate noise amplitude, yielding a peak in spectral power at the forcing frequency.

Misapplication

Assuming that adding noise monotonically improves detection in any system (it requires nonlinearity and a threshold) or attributing observed enhancement in a linear system to stochastic resonance.

Consequence

When present and exploited correctly, stochastic resonance produces an optimal noise level that amplifies weak periodic signals, enabling detection or information transfer that would be impossible in the noise-free subthreshold regime.

Reversal

Deterministic resonance (classical forced resonance) where amplification arises from linear response at a system eigenfrequency, or stochastic anti-resonance where noise decreases coherence.

Boundary

Requires a nonlinear or threshold mechanism and a coherent subthreshold input; does not apply to purely linear systems or to signals without a characteristic timescale; the term typically presumes stationary or quasi‑stationary noise statistics.

Semantic Tension

Often confused with coherence resonance (noise-induced regularity without external periodic forcing) or with linear resonant amplification; the distinction rests on presence/absence of an external periodic input and the role of nonlinearity.

Synthesis

Stochastic resonance is the selective enhancement of a weak periodic signal by appropriately tuned random fluctuations in a nonlinear thresholded system, producing an optimal noise-induced coherence absent in the noise-free case.