Noise-Induced Phenomena: Effects of Noises Based on Tsallis Statistics

Wio, Horacio S.; Deza, Roberto R.

doi:10.1007/978-1-4614-7385-5_3

Cited by 4 publications

(7 citation statements)

References 34 publications

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“…The stationary properties of η (including its autocorrelation function) being thoroughly described elsewhere [4,6,7,8,9], we here summarize the main results. Using the Fokker-Planck formalism, one obtains the stationary probability distribution…”

Section: Q-noise With Tsallis' Statisticsmentioning

confidence: 90%

“…which can be normalized only for q < 3 (Z q is a normalization factor). The first moment η always vanishes [4,6,7,8,9] and the second moment,…”

Section: Q-noise With Tsallis' Statisticsmentioning

confidence: 99%

“…Bounded domain (q < 1) Bounded-domain noise is widespread in nature, and has multiple applications for modeling and control [9] 1 . The infra-Gaussian noise considered here can be addressed as a small deviation from Gaussianity, allowing a perturbative approach.…”

Section: Properties Of the Generated Noisementioning

confidence: 99%

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qNoise: A generator of non-Gaussian colored noise

Deza,

Ihshaish

2018

Preprint

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We introduce a software generator for a class of colored (self-correlated) and non-Gaussian noise, whose statistics and spectrum depend upon only two parameters, q and τ. Inspired by Tsallis' nonextensive formulation of statistical physics, this so-called q-distribution is a handy source of self-correlated noise for a large variety of applications. The q-noise-which tends smoothly for q = 1 to Ornstein-Uhlenbeck noise with autocorrelation τ-is generated via a stochastic differential equation, using the Heun method (a second order Runge-Kutta type integration scheme). The algorithm is implemented as a stand-alone library in c++, available as open source in the Github repository. The noise's statistics can be chosen at will, by varying only parameter q: it has compact support for q < 1 (sub-Gaussian regime) and finite variance up to q = 5/3 (supra-Gaussian regime). Once q has been fixed, the noise's autocorrelation can be tuned up independently by means of parameter τ. This software provides a tool for modeling a large variety of real-world noise types, and is suitable to study the effects of correlation and deviations from the normal distribution in systems of stochastic differential equations which may be relevant for a wide variety of technological applications, as well as for the understanding of situations of biological interest. Applications illustrating how the noise statistics affects the response of a variety of nonlinear systems are briefly discussed. In many of these examples, the system's response turns out to be optimal for some q 1.

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Section: Q-noise With Tsallis' Statisticsmentioning

confidence: 90%

“…which can be normalized only for q < 3 (Z q is a normalization factor). The first moment η always vanishes [4,6,7,8,9] and the second moment,…”

Section: Q-noise With Tsallis' Statisticsmentioning

confidence: 99%

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qNoise: A generator of non-Gaussian colored noise

Deza,

Ihshaish

2018

Preprint

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“…The stationary properties of η (including its autocorrelation function) are thoroughly described elsewhere [8,[10][11][12][13], we here summarize the main results. Using the Fokker-Planck formalism, one obtains the stationary probability distribution…”

Section: Q-noise With Tsallis' Statisticsmentioning

confidence: 92%

qNoise: A generator of non-Gaussian colored noise

Deza

2022

SoftwareX

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“…Namely, the Tsallis q-statistics is obtained in the case of quadratic V (x). For such quadratic potentials, the resulting non-Gaussian bounded process (as well as the case q > 1) has been investigated in a series of influential papers [7][8][9][10][11][12] showing that the departure from the Gaussian PDF in the noise induces remarkable effects in noise-induced transitions and in stochastic resonance [7][8][9]11,13]. This process is sometimes called Tsallis-Borland process [1], although it should be more precisely called the Tsallis-Stariolo-Borland (TSB) process, as we will do in the following.…”

Section: Introductionmentioning

confidence: 99%

Boundedness vs unboundedness of a noise linked to Tsallis q-statistics: The role of the overdamped approximation

Domingo

d’Onofrio

Flandoli

2017

Journal of Mathematical Physics

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An apparently ideal way to generate continuous bounded stochastic processes is to consider the stochastically perturbed motion of a point of small mass in an infinite potential well, under overdamped approximation. Here, however, we show that the aforementioned procedure can be fallacious and lead to incorrect results. We indeed provide a counter-example concerning one of the most employed bounded noises, hereafter called Tsallis-Stariolo-Borland (TSB) noise, which admits the well known Tsallis q-statistics as stationary density. In fact, we show that for negative values of the Tsallis parameter q (corresponding to sufficiently large diffusion coefficient of the stochastic force), the motion resulting from the overdamped approximation is unbounded. We then investigate the cause of the failure of Kramers first type approximation, and we formally show that the solutions of the full Newtonian non-approximated model are bounded, following the physical intuition. Finally, we provide a new family of bounded noises extending the TSB noise, the boundedness of whose solutions we formally show.

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Noise-Induced Phenomena: Effects of Noises Based on Tsallis Statistics

Cited by 4 publications

References 34 publications

qNoise: A generator of non-Gaussian colored noise

qNoise: A generator of non-Gaussian colored noise

qNoise: A generator of non-Gaussian colored noise

Boundedness vs unboundedness of a noise linked to Tsallis q-statistics: The role of the overdamped approximation

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