Controlling Stochastic Resonance

Abstract

We introduce an open-loop control scheme for stochastic resonators; the scheme permits the enhancement or suppression of the spectral response to threshold-crossing events triggered by a timeperiodic signal in background noise. The control is demonstrated in experiments using a Schmitt trigger. A generic two-state theory captures the essential features observed in our experiments and in numerical simulations; this suggests the generality of the effect. [S0031-9007(99)09258-3] PACS numbers: 05.40.Ca, 02.50.Ey, 47.20.Ky, 85.25.Dq Stochastic resonance (SR) is a nonlinear noise-mediated cooperative phenomenon wherein the coherent response to a deterministic signal can be enhanced in the presence of an optimal amount of noise. Since its inception in 1981 [1], SR [2] has been demonstrated in diverse systems including sensory neurons, mammalian neuronal tissue, lasers, SQUIDs, tunnel diodes, and communications devices. Variations and extensions of the classical definition of SR to include aperiodic (e.g., dc or wideband) signals, with the detector response quantified by various information-theoretic [3] or spectral cross-correlation [4] measures, have also appeared in the literature.In this Letter, we introduce a control scheme which allows us, at will, to either enhance or suppress the spectral response in the basic SR effect. Our control strategy is applicable when input information is transmitted via the crossing of either a threshold or potential energy barrier. This raises the intriguing possibility that in situations where external signals might be potentially deleterious, e.g., electromagnetic field interactions with neuronal tissue [5], their effects could be substantially reduced or even eliminated via (externally applied) control signals.The experiments were carried out in a modified Schmitt trigger (ST) electronic circuit. The Schmitt trigger is one of the simplest threshold systems [6,7], possessing a static hysteretic nonlinearity. We denote the lower and upper threshold voltages in the Schmitt trigger by V L and V U , respectively, with 2b being the (static) threshold separation. A subthreshold 64 Hz time-sinusoidal signal S͑t͒ A S sinv S t ͑A S , b͒ and Gaussian noise [8] are applied to the input. For fixed, equal and opposite V L and V U , standard SR curves can be obtained by measuring the output signal power (SP) at the fundamental frequency v S as a function of input noise power [9]. To realize the control scheme we modulate the upper and lower thresholds sinusoidally, V U ͑t͒ b 1 A M sin͑v M t 1 f͒, V L ͑t͒ 2V U ͑t͒, which results in a "breathing" oscillation ( Figs. 1 and 2) of the barriers with frequency v M . We keep the signal and threshold modulating amplitudes fixed such that A M 1 A S , b (no deterministic switching) and investigate the system's response as a function of the phase offset f and the input noise power. Note that in this work we only consider integer frequency ratios n v M ͞v S ͑ 1, 2͒.Our experimental results are shown in the gray-scale plots of Fig. 3, where signal output pow...

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