Stochastic resonance in a bistable system

Fauve, S.; Heslot, F.

doi:10.1016/0375-9601(83)90086-5

Cited by 838 publications

(392 citation statements)

References 4 publications

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“…A weak periodic eccentricity in the Earth's orbit leads to more drastic weather changes than expected due to nonlinear coupling with environmental fluctuations. 28 -30 In electronic systems SR was first demonstrated with a noise driven circuit using a Schmidt trigger 31 -other studies have used tunnel diodes 32 and, more simply, operational amplifiers. 33 SR has also been demonstrated in a wide range of physical and biological systems 25,26 and even social systems.…”

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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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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“…Bistability, often used as a simple framework to study disorder-order (or supercritical-subcritical), is thought to provide a crucial regulating mechanism in different systems, e.g., in electric circuits [17], in various cellular processes such as cycles, differentiation and apoptosis, regulation of heart, brain, etc. [18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Geometric structure and information change in phase transitions

Kim

Hollerbach

2017

Phys. Rev. E

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We propose a toy model for a cyclic order-disorder transition and introduce a geometric methodology to understand stochastic processes involved in transitions. Specifically, our model consists of a pair of forward and backward processes (FPs and BPs) for the emergence and disappearance of a structure in a stochastic environment. We calculate time-dependent probability density functions (PDFs) and the information length L, which is the total number of different states that a system undergoes during the transition. Time-dependent PDFs during transient relaxation exhibit strikingly different behavior in FPs and BPs. In particular, FPs driven by instability undergo the broadening of the PDF with a large increase in fluctuations before the transition to the ordered state accompanied by narrowing the PDF width. During this stage, we identify an interesting geodesic solution accompanied by the self-regulation between the growth and nonlinear damping where the time scale τ of information change is constant in time, independent of the strength of the stochastic noise. In comparison, BPs are mainly driven by the macroscopic motion due to the movement of the PDF peak. The total information length L between initial and final states is much larger in BPs than in FPs, increasing linearly with the deviation γ of a control parameter from the critical state in BPs while increasing logarithmically with γ in FPs. L scales as | ln D| and D −1/2 in FPs and BPs, respectively, where D measures the strength of the stochastic forcing. These differing scalings with γ and D suggest a great utility of L in capturing different underlying processes, specifically, diffusion vs advection in phase transition by geometry. We discuss physical origins of these scalings and comment on implications of our results for bistable systems undergoing repeated order-disorder transitions (e.g., fitness).

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“…Subsequently, a significant body of work has explored applications in a diverse range of fields such neurophysiology [2], quantum systems [3] and signal processing [4]. Experimental work has also demonstrated stochastic resonance in a range of physical systems such as an ac-driven Schmitt trigger [5], a bistable ring laser [6] and more recently MEMS-scale cantilevered beams [7].…”

Section: Introductionmentioning

confidence: 99%

Enhanced vibrational energy harvesting using nonlinear stochastic resonance

McInnes

Gorman

Cartmell

2008

Journal of Sound and Vibration

237

155

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Stochastic resonance has seen wide application in the physical sciences as a tool to understand weak signal amplification by noise. However, this apparently counterintuitive phenomenon does not appear to have been exploited as a tool to enhance vibrational energy harvesting. In this note we demonstrate that by adding periodic forcing to a vibrationally excited energy harvesting mechanism, the power available from the device is apparently enhanced over a mechanism without periodic forcing.In order to illustrate this novel effect, a conceptually simple, but plausible model of such a device is proposed to explore the use of stochastic resonance to enhance vibrational energy harvesting.

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Stochastic resonance in a bistable system

Cited by 838 publications

References 4 publications

Overview: Unsolved problems of noise and fluctuations

Overview: Unsolved problems of noise and fluctuations

Geometric structure and information change in phase transitions

Enhanced vibrational energy harvesting using nonlinear stochastic resonance

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