Theory of stochastic resonance

TLDR

Stochastic resonance describes how increasing input noise can improve output signal-to-noise ratio in bistable systems, with the effect depending on the system’s specific noise‑induced hopping dynamics. The paper presents a detailed theoretical and numerical study of stochastic resonance using a rate‑equation approach. The authors apply this rate‑equation framework to double‑well and two‑state bistable systems and validate the theory with detailed digital simulations. They derive an equation linking output signal‑to‑noise ratio to the noise‑induced hopping rate between the two states.

Abstract

The concept of stochastic resonance has been introduced previously to describe a curious phenomenon in bistable systems subject to both periodic and random forcing: an increase in the input noise can result in an improvement in the output signal-to-noise ratio. In this paper we present a detailed theoretical and numerical study of stochastic resonance, based on a rate equation approach. The main result is an equation for the output signal-to-noise ratio as a function of the rate at which noise induces hopping between the two states. The manner in which the input noise strength determines this hopping rate depends on the precise nature of the bistable system. For this reason, the theory is applied to two classes of bistable systems, the double-well (continuous) system and the two-state (discrete) system. The theory is tested in detail against digital simulations.