Detecting and quantifying temporal correlations in stochastic resonance via information theory measures

We show that Information Theory quantifiers are suitable tools for detecting and for quantifying noise-induced temporal correlations in stochastic resonance phenomena. We use the Bandt & Pompe (BP) method [Phys. Rev. Lett. 88, 174102 (2002)] to define a probability distribution, P, that fully ch...

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Detalles Bibliográficos
Publicado: 2009
Materias:
Bistable potential
Brownian particles
Complex signal
Noise intensities
Optimal level
Quantifying noise
Real-world
Resonant behavior
Shannon entropy
Statistical complexity
Stochastic resonances
Temporal correlations
Temporal sequences
Time interval
Circuit resonance
Information theory
Magnetic resonance
Probability density function
Random processes
Probability distributions
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14346028_v69_n1_p37_Rosso
http://hdl.handle.net/20.500.12110/paper_14346028_v69_n1_p37_Rosso
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_14346028_v69_n1_p37_Rosso
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spelling paper:paper_14346028_v69_n1_p37_Rosso2023-06-08T16:14:37Z Detecting and quantifying temporal correlations in stochastic resonance via information theory measures Bistable potential Brownian particles Complex signal Noise intensities Optimal level Quantifying noise Real-world Resonant behavior Shannon entropy Statistical complexity Stochastic resonances Temporal correlations Temporal sequences Time interval Circuit resonance Information theory Magnetic resonance Probability density function Random processes Probability distributions We show that Information Theory quantifiers are suitable tools for detecting and for quantifying noise-induced temporal correlations in stochastic resonance phenomena. We use the Bandt & Pompe (BP) method [Phys. Rev. Lett. 88, 174102 (2002)] to define a probability distribution, P, that fully characterizes temporal correlations. The BP method is based on a comparison of neighboring values, and here is applied to the temporal sequence of residence-time intervals generated by the paradigmatic model of a Brownian particle in a sinusoidally modulated bistable potential. The probability distribution P generated via the BP method has associated a normalized Shannon entropy, H[P], and a statistical complexity measure, C[P], which is defined as proposed by Rosso et al. [Phys. Rev. Lett. 99, 154102 (2007)]. The statistical complexity quantifies not only randomness but also the presence of correlational structures, the two extreme circumstances of maximum knowledge ("perfect order") and maximum ignorance ("complete randomness") being regarded an "trivial", and in consequence, having complexity C = 0. We show that both, H and C, display resonant features as a function of the noise intensity, i.e., for an optimal level of noise the entropy displays a minimum and the complexity, a maximum. This resonant behavior indicates noise-enhanced temporal correlations in the sequence of residence-time intervals. The methodology proposed here has great potential for the precise detection of subtle signatures of noise-induced temporal correlations in real-world complex signals. © 2009 EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg. 2009 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14346028_v69_n1_p37_Rosso http://hdl.handle.net/20.500.12110/paper_14346028_v69_n1_p37_Rosso
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Bistable potential
Brownian particles
Complex signal
Noise intensities
Optimal level
Quantifying noise
Real-world
Resonant behavior
Shannon entropy
Statistical complexity
Stochastic resonances
Temporal correlations
Temporal sequences
Time interval
Circuit resonance
Information theory
Magnetic resonance
Probability density function
Random processes
Probability distributions
spellingShingle Bistable potential
Brownian particles
Complex signal
Noise intensities
Optimal level
Quantifying noise
Real-world
Resonant behavior
Shannon entropy
Statistical complexity
Stochastic resonances
Temporal correlations
Temporal sequences
Time interval
Circuit resonance
Information theory
Magnetic resonance
Probability density function
Random processes
Probability distributions
Detecting and quantifying temporal correlations in stochastic resonance via information theory measures
topic_facet Bistable potential
Brownian particles
Complex signal
Noise intensities
Optimal level
Quantifying noise
Real-world
Resonant behavior
Shannon entropy
Statistical complexity
Stochastic resonances
Temporal correlations
Temporal sequences
Time interval
Circuit resonance
Information theory
Magnetic resonance
Probability density function
Random processes
Probability distributions
description We show that Information Theory quantifiers are suitable tools for detecting and for quantifying noise-induced temporal correlations in stochastic resonance phenomena. We use the Bandt & Pompe (BP) method [Phys. Rev. Lett. 88, 174102 (2002)] to define a probability distribution, P, that fully characterizes temporal correlations. The BP method is based on a comparison of neighboring values, and here is applied to the temporal sequence of residence-time intervals generated by the paradigmatic model of a Brownian particle in a sinusoidally modulated bistable potential. The probability distribution P generated via the BP method has associated a normalized Shannon entropy, H[P], and a statistical complexity measure, C[P], which is defined as proposed by Rosso et al. [Phys. Rev. Lett. 99, 154102 (2007)]. The statistical complexity quantifies not only randomness but also the presence of correlational structures, the two extreme circumstances of maximum knowledge ("perfect order") and maximum ignorance ("complete randomness") being regarded an "trivial", and in consequence, having complexity C = 0. We show that both, H and C, display resonant features as a function of the noise intensity, i.e., for an optimal level of noise the entropy displays a minimum and the complexity, a maximum. This resonant behavior indicates noise-enhanced temporal correlations in the sequence of residence-time intervals. The methodology proposed here has great potential for the precise detection of subtle signatures of noise-induced temporal correlations in real-world complex signals. © 2009 EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg.
title Detecting and quantifying temporal correlations in stochastic resonance via information theory measures
title_short Detecting and quantifying temporal correlations in stochastic resonance via information theory measures
title_full Detecting and quantifying temporal correlations in stochastic resonance via information theory measures
title_fullStr Detecting and quantifying temporal correlations in stochastic resonance via information theory measures
title_full_unstemmed Detecting and quantifying temporal correlations in stochastic resonance via information theory measures
title_sort detecting and quantifying temporal correlations in stochastic resonance via information theory measures
publishDate 2009
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14346028_v69_n1_p37_Rosso
http://hdl.handle.net/20.500.12110/paper_14346028_v69_n1_p37_Rosso
_version_ 1768541812957380608

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