Stochastic resonance in a parallel array of nonlinear dynamical elements

Abstract

In an uncoupled parallel array of bistable dynamical elements subject to a common noisy subthreshold rectangular signal, the signal-to-noise ratio (SNR) gain can be improved by tuning the internally added array noise. A SNR gain above unity is observed in certain regions of the array noise intensity. The maximum SNR gain is obtained as the size of the array goes to infinity. This form of stochastic resonance (SR), i.e., array SR, is analytically described by introducing a quasi-stationary probability density model, yielding expressions for the transition probability and the stationary autocorrelation function. The analytical results have interpretative value for the mechanism of array SR, and may be of heuristic interest for applying array SR to related signal processing problems. Additionally, the analytical descriptions of an isolated bistable system agree well with numerical results of both conventional SR for a subthreshold rectangular input and residual SR for a slightly suprathreshold signal.