Stochastic resonance in non-dynamical systems without response thresholds

Abstract

The addition of noise to a system can sometimes improve its ability to transfer information reliably. This phenomenon—known as stochastic resonance—was originally proposed to account for periodicity in the Earth's ice ages¹, but has now been shown to occur in many systems in physics and biology^2–4. Recent experimental and theoretical work has shown that the simplest system exhibiting 'stochastic resonance' consists of nothing more than signal and noise with a threshold-triggered device (when the signal plus noise exceeds the threshold, the system responds momentarily, then relaxes to equilibrium to await the next triggering event)^4–6. Here we introduce a class of non-dynamical and threshold-free systems that also exhibit stochastic resonance. We present and analyse a general mathematical model for such systems, in which a sequence of pulses is generated randomly with a probability (per unit time) that depends exponentially on an input. When this input is a sine-wave masked by additive noise, we observe an increase in the output signal-to-noise ratio as the level of noise increases. This result shows that stochastic resonance can occur in a broad class of thermally driven physico-chemical systems, such as semiconductor p–n junctions, mesoscopic electronic devices and voltage-dependent ion channels⁷, in which reaction rates are controlled by activation barriers.