Stochastic resonance with weak monochromatic driving: Gains above unity induced by high-frequency signals

Abstract

Abstract. -We study the effects of a high-frequency (HF) signal on the response of a noisy bistable system to a low-frequency subthreshold sinusoidal signal. We show that, by conveniently choosing the ratio of the amplitude of the HF signal to its frequency, stochastic resonance gains greater than unity can be measured at the low-frequency value. Thus, the addition of the HF signal can entail an improvement in the detection of weak monochromatic signals. The results are explained in terms of an effective model and illustrated by means of numerical simulations.The phenomenon of stochastic resonance (SR) has been studied with growing interest during the last three decades, being found to be of relevance in a great variety of phenomena in physics, chemistry, and the life sciences [1]. Roughly speaking, SR consists in the amplification of a weak, time-dependent signal of interest by the concerted actions of noise and the nonlinearity of the system. Several quantifiers have been used to characterise the SR response of noisy systems in the presence of periodic signals. In particular, the nonmonotonic behaviour of the output signal-to-noise ratio (SNR) with the strength of the noise is a widely accepted signature of SR. In addition, a dimensionless quantity known as the SR gain is usually defined as the ratio of the output SNR over the input SNR. The SNR measures the "quality" of the signal, in terms of the ratio of its "coherent" (periodic) component over its "incoherent" (noisy) component. In turn, the SR gain compares the "qualities" of the output and the input signals. In general, obtaining high output SNRs and SR gains greater than unity would be desirable when using SR as an amplification mechanism. Analog [2,3] and numerical [4,5] simulations have shown that noisy bistable systems driven by subthreshold multifrequency forces can display SR gains greater than unity when the parameters of the problem are properly chosen. Moreover, in [6], a two-state model of SR has been used to explain these results analytically. By contrast, to the best of our knowledge, there is no evidence of SR gains greater than unity when a subthreshold monochromatic signal drives an isolated bistable system. However, these unusual large gains have been reported in the case of a suprathreshold sinusoidal signal for an isolated bistable system [7] and in the case of a subthreshold sinusoidal signal for coupled bistable systems [8].As it has been already pointed out in the literature [7], an improvement of the response of a nonlinear system to a subthreshold signal of interest embedded in noise can be achieved better by lowering the threshold value rather than by increasing the noise strength. However, in most cases of practical interest, threshold lowering is usually a difficult task. Recently, it has been shown that the effect of a strong high-frequency (HF) monochromatic force on the overdamped dynamics of a Brownian particle in a bistable potential can be described in terms of an effective potential whose characteristics depend on the par...

Stochastic resonance in finite arrays of bistable elements with local coupling

“…Those findings indicated that the arrays were indeed operating in nonlinear regimes. Similar results have been reported for single bistable units driven by a suprathreshold sinusoidal force [12], by subthreshold multi-frequency forces [13,14,15,16,17,18], or by a subthreshold sinusoidal force in the presence of a strong, high-frequency monochromatic signal [19]. Nevertheless, to the best of our knowledge, gains larger than unity have never been observed when the single bistable unit is driven by just a subthreshold sinusoidal force.…”

Vibrational Mechanics in an Optical Lattice: Controlling Transport via Potential Renormalization

“…The potential is renormalized, with its amplitude controlled by the strength and frequency of the HF field. The mechanism underlying the potential renormalization is the so-called vibrational resonance, intially introduced [3] and observed [4][5][6][7] in bistable systems. Our experiment uses cold atoms in a dissipative optical lattice as a model system.…”

Finite-size fluctuations and stochastic resonance in globally coupled bistable systems

“…This situation resembles the effect of a high-frequency signal in an isolated bistable system. In the later case, the high-frequency signal can be removed from the description by means of an effective bistable potential with modified parameters, with the consequence that previously subthreshold driving amplitudes can become suprathreshold from the point of view of the effective potential [14]. In contrast, the effective dynamics induced by the high-frequency signal has been shown to provoke the opposite effect on an excitable system, being able to suppress the excitable character of the system [15].…”