The mechanism of stochastic resonance
TL;DR: In this paper, it was 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 perturbations is absent.
Abstract: 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.
Citations
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TL;DR: In this paper, the authors report, extend, and interpret much of our current understanding relating to theories of noise-activated escape, for which many of the notable contributions are originating from the communities both of physics and of physical chemistry.
Abstract: The calculation of rate coefficients is a discipline of nonlinear science of importance to much of physics, chemistry, engineering, and biology. Fifty years after Kramers' seminal paper on thermally activated barrier crossing, the authors report, extend, and interpret much of our current understanding relating to theories of noise-activated escape, for which many of the notable contributions are originating from the communities both of physics and of physical chemistry. Theoretical as well as numerical approaches are discussed for single- and many-dimensional metastable systems (including fields) in gases and condensed phases. The role of many-dimensional transition-state theory is contrasted with Kramers' reaction-rate theory for moderate-to-strong friction; the authors emphasize the physical situation and the close connection between unimolecular rate theory and Kramers' work for weakly damped systems. The rate theory accounting for memory friction is presented, together with a unifying theoretical approach which covers the whole regime of weak-to-moderate-to-strong friction on the same basis (turnover theory). The peculiarities of noise-activated escape in a variety of physically different metastable potential configurations is elucidated in terms of the mean-first-passage-time technique. Moreover, the role and the complexity of escape in driven systems exhibiting possibly multiple, metastable stationary nonequilibrium states is identified. At lower temperatures, quantum tunneling effects start to dominate the rate mechanism. The early quantum approaches as well as the latest quantum versions of Kramers' theory are discussed, thereby providing a description of dissipative escape events at all temperatures. In addition, an attempt is made to discuss prominent experimental work as it relates to Kramers' reaction-rate theory and to indicate the most important areas for future research in theory and experiment.
5,180 citations
TL;DR: How noise affects neuronal networks and the principles the nervous system applies to counter detrimental effects of noise are highlighted, and noise's potential benefits are discussed.
Abstract: Noise — random disturbances of signals — poses a fundamental problem for information processing and affects all aspects of nervous-system function. However, the nature, amount and impact of noise in the nervous system have only recently been addressed in a quantitative manner. Experimental and computational methods have shown that multiple noise sources contribute to cellular and behavioural trial-to-trial variability. We review the sources of noise in the nervous system, from the molecular to the behavioural level, and show how noise contributes to trial-to-trial variability. We highlight how noise affects neuronal networks and the principles the nervous system applies to counter detrimental effects of noise, and briefly discuss noise's potential benefits.
2,350 citations
TL;DR: Synchronization of chaos refers to a process where two chaotic systems adjust a given property of their motion to a common behavior due to a coupling or to a forcing (periodical or noisy) as discussed by the authors.
Abstract: Synchronization of chaos refers to a process wherein two (or many) chaotic systems (either equivalent or nonequivalent) adjust a given property of their motion to a common behavior due to a coupling or to a forcing (periodical or noisy). We review major ideas involved in the field of synchronization of chaotic systems, and present in detail several types of synchronization features: complete synchronization, lag synchronization, generalized synchronization, phase and imperfect phase synchronization. We also discuss problems connected with characterizing synchronized states in extended pattern forming systems. Finally, we point out the relevance of chaos synchronization, especially in physiology, nonlinear optics and fluid dynamics, and give a review of relevant experimental applications of these ideas and techniques.
2,266 citations
TL;DR: In this paper, the authors show that, even at zero temperature, transport of excitations across dissipative quantum networks can be enhanced by local dephasing noise and suggest that the presence of entanglement does not play an essential role for energy transport and may even hinder it.
Abstract: Transport phenomena are fundamental in physics. They allow for information and energy to be exchanged between individual constituents of communication systems, networks or even biological entities. Environmental noise will generally hinder the efficiency of the transport process. However, and contrary to intuition, there are situations in classical systems where thermal fluctuations are actually instrumental in assisting transport phenomena. Here we show that, even at zero temperature, transport of excitations across dissipative quantum networks can be enhanced by local dephasing noise. We explain the underlying physical mechanisms behind this phenomenon and propose possible experimental demonstrations in quantum optics. Our results suggest that the presence of entanglement does not play an essential role for energy transport and may even hinder it. We argue that Nature may be routinely exploiting dephasing noise and show that the transport of excitations in simplified models of light harvesting molecules does benefit from such noise assisted processes. These results point toward the possibility for designing optimized structures for transport, for example in artificial nanostructures, assisted by noise.
941 citations
TL;DR: Stochastic resonance is a ubiquitous and conspicuous phenomenon compatible with neural models and theories of brain function and should encourage neuroscientists and clinical neurophysiologists to explore stochastic resonance in biology and medical science.
Abstract: Objective : To review the stochastic resonance phenomena observed in sensory systems and to describe how a random process (`noise') added to a subthreshold stimulus can enhance sensory information processing and perception. Results : Nonlinear systems need a threshold, subthreshold information bearing stimulus and `noise' for stochastic resonance phenomena to occur. These three ingredients are ubiquitous in nature and man-made systems, which accounts for the observation of stochastic resonance in fields and conditions ranging from physics and engineering to biology and medicine. The stochastic resonance paradigm is compatible with single-neuron models or synaptic and channels properties and applies to neuronal assemblies activated by sensory inputs and perceptual processes as well. Here we review a few of the landmark experiments (including psychophysics, electrophysiology, fMRI, human vision, hearing and tactile functions, animal behavior, single/multiunit activity recordings). Models and experiments show a peculiar consistency with known neuronal and brain physiology. A number of naturally occurring `noise' sources in the brain (e.g. synaptic transmission, channel gating, ion concentrations, membrane conductance) possibly accounting for stochastic resonance phenomena are also reviewed. Evidence is given suggesting a possible role of stochastic resonance in brain function, including detection of weak signals, synchronization and coherence among neuronal assemblies, phase resetting, `carrier' signals, animal avoidance and feeding behaviors. Conclusions : Stochastic resonance is a ubiquitous and conspicuous phenomenon compatible with neural models and theories of brain function. The available evidence suggests cautious interpretation, but justifies research and should encourage neuroscientists and clinical neurophysiologists to explore stochastic resonance in biology and medical science.
874 citations
References
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TL;DR: In this paper, it was shown that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into considerably different states, and systems with bounded solutions are shown to possess bounded numerical solutions.
Abstract: Finite systems of deterministic ordinary nonlinear differential equations may be designed to represent forced dissipative hydrodynamic flow. Solutions of these equations can be identified with trajectories in phase space For those systems with bounded solutions, it is found that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into considerably different states. Systems with bounded solutions are shown to possess bounded numerical solutions.
16,554 citations
TL;DR: In this paper, a review of new ideas on the nature of the unpredictable turbulent motions in dissipative media connected with the discovery of strange attractors, i.e., attractive regions in phase space within which all paths are unstable and behave in a very complex fashion.
Abstract: Until quite recently, it was thought that turbulence, i.e., stochastic self-oscillations of a continuous medium, was related exclusively to the excitation of an exceedingly large number of degrees of freedom. This review is devoted to the discussion of new ideas on the nature of the unpredictable turbulent motions in dissipative media connected with the discovery of strange attractors, i.e., attractive regions in phase space within which all paths are unstable and behave in a very complex fashion (motions on an attractor of this kind are characterized by a continuous spectrum). Turbulence represented by a strange attractor is described by a finite number of degrees of freedom, i.e., modes whose physical nature may be different. The example of a simple electronic noise generator is used to illustrate how the instability (divergence) of such paths leads to stochastic behavior. The analysis is based on the introduction of a nonreciprocally single-valued Poincare mapping onto itself, which is then used to describe the strange attractors encountered in different physical problems. An example of this mapping is used to demonstrate the discrete, symbolic, description of dynamic systems. The properties of such systems which indicate their stochastic nature, for example, positive topologic entropy and hyperbolicity are discussed. Specific physical mechanisms leading to the appearance of stochastic behavior and characterized by a continuous time spectrum are discussed. Strange attractors that appear in the case of parametric instability of waves in plasmas, laser locking by an external field, and so on, are demonstrated. "Attractor models" of hydrodynamic turbulence are reviewed, and in particular, finite-dimensional hydrodynamic models of convection in a layer and of Couette flow between rotating cylinders are constructed and found to exhibit stochastic behavior.
96 citations
"The mechanism of stochastic resonan..." refers methods in this paper
...This model has been used by several authors as a prototype of the transition to chaos in deterministic dynamical systems, and it is a prototype for the transition to turbulence as well as laser dynamics (see Rabinovich (1978) for a detailed discussion)....
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TL;DR: In this paper, the effect of external random forces on the static and dynamic behavior of the Lorenz model is investigated and results of a numerical calculation in the conductive, convective, and turbulent regimes are reported.
Abstract: The effect of external random forces on the static and dynamic behavior of the Lorenz model is investigated. Results of a numerical calculation in the conductive, convective, and turbulent regimes are reported. The properties of static and time-dependent correlation functions of the three degrees of freedom of the model are analyzed for varying strength of the external noise level and compared with the behavior of the unforced system.
32 citations
"The mechanism of stochastic resonan..." refers methods in this paper
...However, a qualitative discussion can be performed using recent investigations of Sutera (1980) and Zippelius and Lucke (1981)....
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TL;DR: In this paper, a simple truncated spectral model of a fluid in a pure convective motion due to Lorenz (1963) was studied and it was shown that where the equations are perturbed by a stochastic Wiener process (white noise), the system leaves the attraction domain of stable steady state after a time τ+
Abstract: In this note we study a simple truncated spectral model of a fluid in a pure convective motion due to Lorenz (1963). We find that where the equations are perturbed by a stochastic Wiener process (white noise), the system leaves the attraction domain of stable steady state after a time τ+.
31 citations
"The mechanism of stochastic resonan..." refers methods in this paper
...However, a qualitative discussion can be performed using recent investigations of Sutera (1980) and Zippelius and Lucke (1981)....
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TL;DR: The general Fokker-Planck equation for forward Hopf bifurcation of an oscillatory mode under the influence of multiplicative gaussian white noise was solved exactly as discussed by the authors.
Abstract: The general Fokker-Planck equation for forward Hopf bifurcation of an oscillatory mode under the influence of multiplicative gaussian white noise is solved exactly.
8 citations
"The mechanism of stochastic resonan..." refers background in this paper
...We believe that this mechanism can also be important for those systems showing Hopf bifurcation and stochastic forcing, as recently described by Graham (1980)....
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