Stochastic resonance in threshold devices

Reviews of Modern Physics, 1998

Fluctuation and Noise Letters, 2002

It is demonstrated that benefits from the noise can be gained at various levels in stochastic resonance. Raising the noise can produce signal amplification as well as signal-tonoise ratio improvement, input-output gain exceeding unity in signal-to-noise ratio, and enhanced performance in optimal processing. This series of benefits is successively exhibited in the processing of a periodic signal coupled to a white noise through essentially static nonlinearities. Especially, it is established that noise benefits in stochastic resonance can extend up to optimal processing, by considering an optimal Bayesian detector whose performance is improvable by raising the level of the noise.

Physical review. E, Statistical, nonlinear, and soft matter physics, 2003

We analyze the parametric estimation that can be performed on a signal buried in noise based on the parsimonious representation provided by a parallel array of threshold devices. The Fisher information contained in the array output about the input parameter is used as the measure of performance in the estimation task. For estimation on a suprathreshold input signal, we establish that enhancement of the Fisher information can be obtained by addition of independent noises to the thresholds in the array. Similar improvement by noise is also shown to be possible for the estimation error of the maximum likelihood estimator. These results extend the applicability of the recently introduced nonlinear phenomenon of suprathreshold stochastic resonance.

IEEE Transactions …, 2002

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, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 1999

A subthreshold signal may be detected if noise is added to the data. We study a simple model, consisting of a constant signal to which at uniformly spaced times independent and identically distributed noise variables with known distribution are added. A detector records the times at which the noisy signal exceeds a threshold. There is an optimal noise level, called stochastic resonance. We explore the detectability of the signal in a system with one or more detectors, with different thresholds. We use a statistical detectability measure, the asymptotic variance of the best estimator of the signal from the thresholded data, or equivalently, the Fisher information in the data. In particular, we determine optimal configurations of detectors, varying the distances between the thresholds and the signal, as well as the noise level. The approach generalizes to nonconstant signals.

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.

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, Statistical, nonlinear, and soft matter physics, 2003

We study systems which combine both oscillatory and excitable properties, and hence intrinsically possess two internal frequencies, responsible for standard spiking and for small amplitude oscillatory limit cycles (Canard orbits). We show that in such a system the effect of stochastic resonance can be amplified by application of an additional high-frequency signal, which is in resonance with the oscillatory frequency. It is important that for this amplification one needs much lower noise intensities as for conventional stochastic resonance in excitable systems.

Physical Review Letters, 2002

In order to test theoretical predictions, we have studied the phenomenon of stochastic resonance in an electronic experimental system driven by white non Gaussian noise. In agreement with the theoretical predictions our main findings are: an enhancement of the sensibility of the system together with a remarkable widening of the response (robustness). This implies that even a single resonant unit can reach a marked reduction in the need of noise tuning.

Fluctuation and Noise Letters, 2003

We analyze stochastic resonance in systems driven by non-Gaussian noises. For the bistable double well we compare the signal-to-noise ratio resulting from numerical simulations with some quasi-analytical results predicted by a consistent Markovian approximation in the case of a colored non-Gaussian noise. We also study the FitzHugh-Nagumo excitable system in the presence of the same noise. In both systems, we find that, as the noise departs from Gaussian behavior, there is a regime (different for the excitable and the bistable systems) in which there is a notable robustness against noise tuning since the signal-to-noise ratio curve broadens and becomes less sensitive to the actual value of the noise intensity. We also compare our results with some experiments in sensory systems.

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.

Physical Review A, 1991

Stochastic resonance is a cooperative effect of noise and periodic driving in bistable systems. It can be used for the detection and amplification of weak signals embedded within a large noise background. In doing so, the noise triggers the transfer of power to the signal. In this paper we first present general properties of periodically driven Brownian motion, such as the long-time behavior of correlation functions and the existence of a "supersymmetric" partner system. Within the framework of nonstationary stochastic processes, we present a careful numerical study of the stochastic resonance effect, without restrictions on the modulation amplitude and frequency. In particular, in the regime of intermediate driving frequencies which has not yet been covered by theories, we have discovered a secondary resonance at smaller values of the noise strength.

Proceedings of 27th Asilomar Conference on Signals, Systems and Computers, 1993

Stochastic Resonance is a nonlinear stochastic phenomenon which can cause a transfer of energy from a random process (noise) to a periodic signal over a certain range of signal and system parameters. It has been observed in many diverse natural andphysical systems, and may be one means by which biological sensor systems amplify weak sensory signals for detection. This paper is an evaluation of the use qf the Stochastic Resonance phenomenon as a tool for signal processing in terms of its processing gain.

Forbidden interval theorems state whether a stochastic-resonance noise benefit occurs based on whether the average noise value falls outside or inside an interval of parameter values. Such theorems act as a type of screening device for mutual-information noise benefits in the detection of subthreshold signals. Their proof structure reduces the search for a noise benefit to the often simple task of showing that a zero limit exists. This chapter presents the basic forbidden interval theorem for threshold neurons and four applications of increasing complexity. The first application shows that small amounts of electrical noise can help a carbon nanotube detect faint electrical signals. The second application extends the basic forbidden interval theorem to quantum communication through the judicious use of squeezed light. The third application extends the theorems to noise benefits in standard models of spiking retinas. The fourth application extends the noise benefits in retinal and other neuron models to Levy noise that generalizes Brownian motion and allows for jump and impulsive noise processes.