Gain in stochastic resonance: Precise numerics versus linear response theory beyond the two-mode approximation

We investigate the role of noise in the phenomenon of stochastic synchronization of switching events in a rocked, overdamped bistable potential driven by white Gaussian noise, the archetype description of Stochastic Resonance. We present a new approach to the stochastic counting process of noise-induced switching events: starting from the Markovian dynamics of the nonstationary, continuous particle dynamics one finds upon contraction onto two states a non-Markovian renewal dynamics. The output frequency is determined as the velocity of the underlying discrete phase dynamics. The phenomenon of noise-assisted phase synchronization is investigated in terms of an effective, instantaneous phase diffusion. The theory is applied to rectangular-shaped rocking signals versus increasing input-noise strengths. Precise numerical simulations corroborate very favorably our analytical results. The novel theoretical findings are also compared with prior findings.

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“…[28]), we have integrated Eq. (1) for a large number of noise realizations, M , starting from one of the minima q α0 (0).…”

Section: A Comparison With Numerical Resultsmentioning

confidence: 99%

Theory of frequency and phase synchronization in a rocked bistable stochastic system

et al. 2005

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“…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.…”

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confidence: 99%

“…2 we depict the dependence on the noise strength D of the SR gain in a bistable noisy system driven by a sinusoidal subthreshold signal, both in the absence (empty diamonds) and presence (full diamonds) of an HF signal. The SR gain has been evaluated numerically following the method described in [4]. The parameter values of the sinusoidal subthreshold signal are A = 0.1 and Ω = 0.005.…”

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

Casado‐Pascual¹,

Cubero²,

Baltanás³

2007

Europhys. Lett.

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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...

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“…Another approach has been studied recently for SNR amplification in nonlinear devices, based on the phenomenon of stochastic resonance. So far in this context, it is the static nonlinearities that have been shown to be the most effective (as opposed to dynamic nonlinearities) for SNR amplification of a sinusoid in Gaussian white noise [10], [3], [6]. The two approaches can be contrasted as follows.…”

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confidence: 99%

Nonlinear Devices Acting as SNR Amplifiers for a Harmonic Signal in Noise

Chapeau‐Blondeau

Rousseau

2006

Circuits Syst Signal Process

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Abstract. A harmonic signal corrupted by an additive white noise is processed by an arbitrary memoryless nonlinear device. The transformation of the signal-to-noise ratio (SNR) by the nonlinearity is explicitly computed and analyzed for Gaussian and non-Gaussian noise. Simple nonlinearities, easily implementable as electronic circuits, are shown capable of producing an amplification of the SNR. Such an amplification is not obtainable with linear filters, whatever their complexity or high order, but becomes easily accessible with simple nonlinear devices.

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Gain in stochastic resonance: Precise numerics versus linear response theory beyond the two-mode approximation

Cited by 46 publications

References 28 publications

Theory of frequency and phase synchronization in a rocked bistable stochastic system

Theory of frequency and phase synchronization in a rocked bistable stochastic system

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

Nonlinear Devices Acting as SNR Amplifiers for a Harmonic Signal in Noise

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