Analytical study of coupled two-state stochastic resonators

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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 analyzed and array-enhanced stochastic resonance is established for pure as well as noisy periodic signals. The coupling-induced improvement of the signal-to-noise ratio compared to an uncoupled element is shown to be limited by a factor 4, which is only reached for vanishing input noise.
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