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 ages, but has now been shown to occur in many systems in physics and biology. 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). 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 channels, in which reaction rates are controlled by activation barriers.