Stochastic resonance: Noise-enhanced phase coherence

Jetp Letters, 1993

High frequency stochastic resonance (SR) phenomena, associated with fluctuational transitions between coexisting periodic attractors, have been investigated experimentally in an electronic model of a single-well Duffing oscillator bistable in a nearly resonant field of frequency $\omega_F$. It is shown that, with increasing noise intensity, the signal/noise ratio (SNR) for a signal due to a weak trial force of frequency $\Omega \sim \omega_F$ at first decreases, then {\it increases}, and finally decreases again at higher noise intensities: behaviour similar to that observed previously for conventional (low frequency) SR in systems with static bistable potentials. The stochastic enhancement of the SNR of an additional signal at the mirror-reflected frequency $\vert \Omega - 2 \omega_F \vert$ is also observed, in accordance with theoretical predictions. Relationships with phenomena in nonlinear optics are discussed.

1993

Suppose one wants to look at a weak periodic signal within a random noise: a way to improve the Signal to Noise Ratio (SNR) is to use a lock-in amplifier, but the frequency of the periodic component must be known to achieve a high amplification. A different method is offered by the mechanism of Stochastic Resonance (SR) 1.2.

Journal of Physics A: Mathematical and General, 1981

It is shown that a dynamical system subject to both periodic forcing and random perturbation may show a resonance (peak in the power spectrum) which is absent when either the forcing or the perturbation is absent.

Contemporary Physics, 2012

Nonlinear systems driven by noise and periodic forces with more than one frequency exhibit the phenomenon of Ghost Stochastic Resonance (GSR) found in a wide and disparate variety of fields ranging from biology to geophysics. The common novel feature is the emergence of a "ghost" frequency in the system's output which it is absent in the input. As reviewed here, the uncovering of this phenomenon helped to understand a range of problems, from the perception of pitch in complex sounds or visual stimuli, to the explanation of climate cycles. Recent theoretical efforts show that a simple mechanism with two ingredients are at work in all these observations. The first one is the linear interference between the periodic inputs and the second a nonlinear detection of the largest constructive interferences, involving a noisy threshold. These notes are dedicated to review the main aspects of this phenomenon, as well as its different manifestations described on a bewildering variety of systems ranging from neurons, semiconductor lasers, electronic circuits to models of glacial climate cycles.

Physical Review E, 2000

We investigate the stochastic resonance phenomenon in a physical system based on a tunnel diode. The experimental control parameters are set to allow the control of the frequency and amplitude of the deterministic modulating signal over an interval of values spanning several orders of magnitude. We observe both a regime described by the linear-response theory and the nonlinear deviation from it. In the nonlinear regime we detect saturation of the power spectral density of the output signal detected at the frequency of the modulating signal and a dip in the noise level of the same spectral density. When these effects are observed we detect a phase and frequency synchronization between the stochastic output and the deterministic input.

Physical Review Letters, 1999

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 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 or spectral cross-correlation measures, have also appeared in the literature.

Circuits and Systems …, 1999

Stochastic resonance (SR), in which a periodic signal in a nonlinear system can be amplified by added noise, is discussed. The application of circuit modeling techniques to the conventional form of SR, which occurs in static bistable potentials, was considered in a companion paper. Here, the investigation of nonconventional forms of SR in part using similar electronic techniques is described. In the small-signal limit, the results are well described in terms of linear response theory. Some other phenomena of topical interest, closely related to SR, are also treated.

Circuits and Systems …, 1999

Stochastic resonance (SR), a phenomenon in which a periodic signal in a nonlinear system can be amplified by added noise, is introduced and discussed. Techniques for investigating SR using electronic circuits are described in practical terms. The physical nature of SR, and the explanation of weak-noise SR as a linear response phenomenon, are considered. Conventional SR, for systems characterized by static bistable potentials, is described together with examples of the data obtainable from the circuit models used to test the theory.

Physical Review E, 2000

The concept of controlling stochastic resonance has been recently introduced ͓L. Gammaitoni et al., Phys. Rev. Lett. 82, 4574 ͑1999͔͒ to enhance or suppress the spectral response to threshold-crossing events triggered by a time-periodic signal in background noise. Here, we develop a general theoretical framework, based on a rate equation approach. This generic two-state theory captures the essential features observed in our experiments and numerical simulations.

Reviews of Modern Physics, 1998