Non-Dynamical Stochastic Resonance: Theory and Experiments with White and Arbitrarily Coloured Noise

Gingl, Zoltán; Kiss, L.B.; Moss, Frank

doi:10.1209/0295-5075/29/3/001

Cited by 258 publications

(183 citation statements)

References 22 publications

(7 reference statements)

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“…Other studies have shown that intrinsic noise can be responsible for the appearance of stochastic resonance [5,13] and aperiodic stochastic resonance [14] in nondynamical systems. In those studies, external noise enhances the response of the system to a periodic or an aperiodic signal.…”

Section: (Received 22 May 2000)mentioning

confidence: 99%

Noise Suppression by Noise

Vilar

Rubı́

2001

Phys. Rev. Lett.

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We have analyzed the interplay between an externally added noise and the intrinsic noise of systems that relax fast towards a stationary state, and found that increasing the intensity of the external noise can reduce the total noise of the system. We have established a general criterion for the appearance of this phenomenon and discussed two examples in detail. DOI: 10.1103/PhysRevLett.86.950 PACS numbers: 05.40.Ca, 05.40. -a For a long time, noise was considered to be only a source of disorder, a nuisance to be avoided. Recently, this view has been changing due to several phenomena that show constructive facets of noise. Among them, the most widely studied is the phenomenon of stochastic resonance, where the addition of noise to a system enhances its response to a periodic force [1,2]. This counterintuitive aspect of noise has been found under a wide variety of situations, including bistable [3] and monostable [4] systems, nondynamical elements with [5] and without [6] threshold, and pattern forming systems [7]. Similar constructive outcomes are also found in other remarkable phenomena, such as noise induced transitions [8] and noise induced transport [9]. To some extent, the presence of noise is an unavoidable feature, and as one moves from macroscopic to microscopic scales that presence becomes more and more prominent. To withdraw the noise, it is customary to reduce as much as possible all of the external noise sources that affect the system since it still seems paradoxical that adding noise might result in a less noisy system.In this Letter we show that the intrinsic noise displayed by some systems can substantially be reduced through its nonlinear interplay with externally added noise and we establish sufficient conditions for this phenomenon to occur. The systems we consider are those relaxing fast to a stationary state where their properties are completely determined by some parameters: the state of the system, denoted by I͑t, V͒, is a function of some input parameters, denoted by the set V. These systems are usually called nondynamical systems. For the sake of simplicity, we consider the case of a single input parameter, i.e., V ϵ V . The temporal dependence of the state of the system takes into account the intrinsic fluctuations. This stochastic behavior can be described by the mean value ͗I͑t, V ͒͘ H͑V ͒and the correlation functionwhere ͗.͘ indicates average over the noise. For practical purposes, it is convenient to write I͑V , t͒ aswhere j͑t, V ͒, with ͗j͑t, V ͒j͑t 1 t, V ͒͘ G ͑V , t͒, represents the intrinsic noise. When the characteristic time scales of the fluctuations are smaller than any other entering the system,G͑V , t͒ G͑V ͒d͑t͒, and the power spectrum of the fluctuations is flat for the range of frequencies of interest. The function H͑V ͒ corresponds to the deterministic response and G͑V ͒ corresponds to the intensity of the intrinsic fluctuations.We now analyze how adding external noise affects the output of the system. We consider that a random quantity z ͑t͒ is added to a constant in...

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Section: (Received 22 May 2000)mentioning

confidence: 99%

Noise Suppression by Noise

Vilar

Rubı́

2001

Phys. Rev. Lett.

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“…However, in recent years this has been rather like trying to shoot a moving target. At first, SR was thought to be a property of bistable systems, then it was observed in a simple thresholding element, 35 and it is now shown that not even a threshold operation is required. 36 Even more recent viewpoints generalize SR as a nonlinear filtering phenomenon 37 or a natural feature of any nonlinear system with a large, strongly noisedependent susceptibility.…”

Section: Stochastic Resonancementioning

confidence: 99%

Overview: Unsolved problems of noise and fluctuations

Abbott

2001

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Noise and fluctuations are at the seat of all physical phenomena. It is well known that, in linear systems, noise plays a destructive role. However, an emerging paradigm for nonlinear systems is that noise can play a constructive role-in some cases information transfer can be optimized at nonzero noise levels. Another use of noise is that its measured characteristics can tell us useful information about the system itself. Problems associated with fluctuations have been studied since 1826 and this Focus Issue brings together a collection of articles that highlight some of the emerging hot unsolved noise problems to point the way for future research. © 2001 American Institute of Physics. ͓DOI: 10.1063/1.1398543͔The study of fluctuations crosses many discipline boundaries as ''noise'' is a ubiquitous phenomenon. Noise is traditionally thought of as an unwanted effect that degrades the performance of a system. However, the emerging paradigm now recognizes that noise can play both a destructive or constructive role, depending on the circumstances. Thus there is now an intense interest in noise in many biological, physical, and other systems. The collection of papers in this Focus Issue examines open problems and debates surrounding the role of noise in both chaotic and nonchaotic systems. In this Overview we introduce the concepts of stochastic resonance, Brownian ratchets, 1Õf noise and vacuum fluctuations, and some problems surrounding them.

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“…In the classical situation, SR consists of an optimization by noise of the response of a bistable system to a weak periodic signal. Besides this standard scenario, SR has also been found in monostable [10], excitable [11], nondynamical [12], and thresholdless [13] systems, in systems without an external force (what is called coherence resonance) [14,15], and in systems with transient noiseinduced structure [16].…”

mentioning

confidence: 99%

Noise Induced Propagation in Monostable Media

et al. 2001

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We show that external fluctuations are able to induce propagation of harmonic signals through monostable media. This property is based on the phenomenon of doubly stochastic resonance, where the joint action of multiplicative noise and spatial coupling induces bistability in an otherwise monostable extended medium, and additive noise resonantly enhances the response of the system to a harmonic forcing. Under these conditions, propagation of the harmonic signal through the unforced medium is observed for optimal intensities of the two noises. This noise-induced propagation is studied and quantified in a simple model of coupled nonlinear electronic circuits.

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Non-Dynamical Stochastic Resonance: Theory and Experiments with White and Arbitrarily Coloured Noise

Cited by 258 publications

References 22 publications

Noise Suppression by Noise

Noise Suppression by Noise

Overview: Unsolved problems of noise and fluctuations

Noise Induced Propagation in Monostable Media

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