Statistical distribution and stochastic resonance in a periodically driven chemical system

Dykman, M. I.; Horita, Takehiko; Ross, John

doi:10.1063/1.469796

Cited by 56 publications

(43 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…So a great deal of SR research has focused on how dither-like noise can help spiking neurons process data streams [12], [33], [38]. SR occurs in physical systems such as ring lasers [56], threshold hysteretic Schmitt triggers [27], superconducting quantum interference devices (SQUIDs) [36], Josephson junctions [7], chemical systems [25], and quantum-mechanical systems [34]. SR also occurs in biological systems such as the rat [18], crayfish [23], cricket [48], river paddlefish [66], and in many types of model neurons [8], [10], [16], [17], [63].…”

mentioning

confidence: 99%

Adaptive Stochastic Resonance in Noisy Neurons Based on Mutual Information

Mitaim

Kosko

2004

IEEE Trans. Neural Netw.

105

View full text Add to dashboard Cite

Abstract-Noise can improve how memoryless neurons process signals and maximize their throughput information. Such favorable use of noise is the so-called "stochastic resonance" or SR effect at the level of threshold neurons and continuous neurons. This paper presents theoretical and simulation evidence that 1) lone noisy threshold and continuous neurons exhibit the SR effect in terms of the mutual information between random input and output sequences, 2) a new statistically robust learning law can find this entropy-optimal noise level, and 3) the adaptive SR effect is robust against highly impulsive noise with infinite variance. Histograms estimate the relevant probability density functions at each learning iteration. A theorem shows that almost all noise probability density functions produce some SR effect in threshold neurons even if the noise is impulsive and has infinite variance. The optimal noise level in threshold neurons also behaves nonlinearly as the input signal amplitude increases. Simulations further show that the SR effect persists for several sigmoidal neurons and for Gaussian radial-basis-function neurons.Index Terms-Alpha-stable noise, impulsive noise, infinite-variance statistics, mutual information, noise processing, sigmoidal neurons and radial basis functions, stochastic gradient learning, stochastic resonance (SR), threshold neurons. I. NOISE AND ADAPTIVE STOCHASTIC RESONANCE NOISE is an unwanted signal or source of energy. Scientists and engineers have largely tried to filter noise or cancel it or mask it out of existence. The Noise Pollution Clearinghouse condemns noise outright: "Noise is unwanted sound. It is derived from the Latin word 'nausea' meaning seasickness. Noise is among the most pervasive pollutants today. Noise from road traffic, jet planes, jet skis, garbage trucks, construction equipment, manufacturing processes, lawn mowers, leaf blowers, and boom boxes, to name a few, are among the unwanted sounds that are routinely broadcast into the air."The Fig. 1 shows how uniform pixel noise can improve our subjective perception of an image. The system quantizes the original gray-scale "Lena" image into a binary image of black and white pixels. It emits a white pixel as output if the input gray-scale pixel equals or exceeds a threshold. It emits a black pixel as output if the input gray-scale pixel falls below the threshold. This quantizer is biased because it does not set the threshold at the midpoint of the gray scale. So the quantized version of the original image contains almost no information. A small level of noise sharpens the image contours and helps fill in features when it adds to the original image before the system applies the threshold. Too much noise swamps the image and degrades its contours. Gammaitoni [29] and others [70] have proposed a dithering argument for this SR effect and still others [55] have applied this argument to still images. The argument involves adding dither noise to a signal before quantization. Consider gray-scale pixel and binary output pixel wi...

show abstract

mentioning

confidence: 99%

Adaptive Stochastic Resonance in Noisy Neurons Based on Mutual Information

Mitaim

Kosko

2004

IEEE Trans. Neural Netw.

105

View full text Add to dashboard Cite

show abstract

“…Using the linear response theory, some alternative types of SR turned out. For details, see the original papers by Dykman [19,85,86], Luchinsky [7,8], and other authors. They identified SR existence in quite different systems from those commonly studied to date, which are typical by a static double-well potential and being excited by a force equal to the sum of periodic and driving stochastic components.…”

Section: Alternative Differential Operatorsmentioning

confidence: 99%

Stochastic Resonance and Related Topics

Náprstek¹,

Fischer²

2017

Resonance

View full text Add to dashboard Cite

The stochastic resonance (SR) is the phenomenon which can emerge in nonlinear dynamic systems. In general, it is related with a bistable nonlinear system of Duffing type under additive excitation combining deterministic periodic force and Gaussian white noise. It manifests as a stable quasiperiodic interwell hoppingbetweenbothstablestateswithasmall random perturbation. Classical definition and basic features of SR are regarded. The most important methods of investigation outlined are: analytical, semi-analytical, and numerical procedures of governing physical systems or relevant Fokker-Planck equation. Stochastic simulation is mentioned and experimental way of results verification is recommended. Some areas in Engineering Dynamics related with SR are presented together with a particular demonstration observed in the aeroelastic stability. Interaction of stationary and quasiperiodic parts of the response is discussed. Some nonconventional definitions are outlined concerning alternative operators and driving processes are highlighted. The chapter shows a large potential of specific basic, applied and industrial research in SR. This strategy enables to formulate new ideas for both development of nonconventional measures for vibration damping and employment of SR in branches, where it represents an operating mode of the system itself. Weaknesses and empty areas where the research effort of SR should be oriented are indicated.

show abstract

“…So the full picture would be, for small noise, the random walker will be at a neighborhood of the origin with a large probability but with a small probability large deviations might appear and drive the system further away. The probability P with which these large deviations, which promote trajectories (8), manifest themselves into the system dynamics is proportional to the exponential of the negative of the action…”

Section: Large Deviations 21 Brownian Motionmentioning

confidence: 99%

“…The selection of an adequate variable has to be supplemented with selecting a suitable approximation in order to get an operative theory that allows studying the otherwise commonly untractable master equation. A particularly advantageous choice is the analog of the quantum mechanical Wentzel-Kramers-Brillouin (WKB) approximation adapted to this sort of systems, which is now well established in both physical and mathematical literatures, see for instance [3,4,5,6,7,8,9,10,11,12,13,14,15]. It allows the description of both the short time dynamics, which is to a large extent independent of the fluctuations and therefore captured by mean-field type approximations, and the long time behavior which is affected, dramatically on occasion, by large deviations.…”

Section: Introductionmentioning

confidence: 99%

Chemical Oscillations out of Chemical Noise

Escudero¹,

Rivera²,

Torres³

2011

SIAM J. Appl. Dyn. Syst.

View full text Add to dashboard Cite

The dynamics of one species chemical kinetics is studied. Chemical reactions are modelled by means of continuous time Markov processes whose probability distribution obeys a suitable master equation. A large deviation theory is formally introduced, which allows developing a Hamiltonian dynamical system able to describe the system dynamics. Using this technique we are able to show that the intrinsic fluctuations, originated in the discrete character of the reagents, may sustain oscillations and chaotic trajectories which are impossible when these fluctuations are disregarded. An important point is that oscillations and chaos appear in systems whose mean-field dynamics has too low a dimensionality for showing such a behavior. In this sense these phenomena are purely induced by noise, which does not limit 1 arXiv:1004.2722v2 [cond-mat.stat-mech] 2 Oct 2011 itself to shifting a bifurcation threshold. On the other hand, they are large deviations of a short transient nature which typically only appear after long waiting times. We also discuss the implications of our results in understanding extinction events in population dynamics models expressed by means of stoichiometric relations.

show abstract

Statistical distribution and stochastic resonance in a periodically driven chemical system

Cited by 56 publications

References 18 publications

Adaptive Stochastic Resonance in Noisy Neurons Based on Mutual Information

Adaptive Stochastic Resonance in Noisy Neurons Based on Mutual Information

Stochastic Resonance and Related Topics

Chemical Oscillations out of Chemical Noise

Contact Info

Product

Resources

About