An Analytical Study of Coupled Two-State Stochastic Resonators

TL;DR

This paper extends the two-state stochastic resonance model to a chain of coupled elements using Glauber's Ising model, deriving analytical expressions for spectral power amplification and SNR, and analyzing how coupling enhances stochastic resonance.

Contribution

It introduces a coupled chain model of stochastic resonators and provides analytical insights into the effects of coupling on signal amplification and noise performance.

Findings

Coupling can enhance stochastic resonance effects.

Analytical expressions for spectral power amplification and SNR are derived.

Maximum SNR improvement factor is four, achieved with no input noise.

Abstract

The two-state model of stochastic resonance is extended to a chain of coupled two-state elements governed by the dynamics of Glauber's stochastic Ising model. Appropriate assumptions on the model parameters turn the chain into a prototype system of coupled stochastic resonators. In a weak-signal limit analytical expressions are derived for the spectral power amplification and the signal-to-noise ratio of a two-state element embedded into the chain. The effect of the coupling between the elements on both quantities is analysed and array-enhanced stochastic resonance is established for pure as well as noisy periodic signals. The coupling-induced improvement of the SNR compared to an uncoupled element is shown to be limited by a factor four which is only reached for vanishing input noise.