Detecting low-dimensional chaos by the “noise titration” technique: Possible problems and remedies

Gao, Jianbo; Hu, Jing; Mao, Xiang; Tung, Wen‐wen

doi:10.1016/j.chaos.2011.12.004

Cited by 21 publications

(25 citation statements)

References 62 publications

(97 reference statements)

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“…13 Since then, SDLE is used in various fields of research for characterizing the dynamic complexity of the time series signals. [47][48][49][50][51][52][53] SDLE can efficiently characterize the embedded dynamics in complex time series by identifying chaos, noisy chaos, stochastic oscillations, random 1/f process, random levy process, and complex time series with multiple scaling behaviors. Moreover, it is robust to nonstationarity.…”

Section: Scale Dependent Lyapunov Exponentmentioning

confidence: 99%

On the dynamics of ocean ambient noise: Two decades later

Siddagangaiah

Guo

et al. 2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Two decades ago, it was shown that ambient noise exhibits low dimensional chaotic behavior. Recent new techniques in nonlinear science can effectively detect the underlying dynamics in noisy time series. In this paper, the presence of low dimensional deterministic dynamics in ambient noise is investigated using diverse nonlinear techniques, including correlation dimension, Lyapunov exponent, nonlinear prediction, and entropy based methods. The consistent interpretation of different methods demonstrates that ambient noise can be best modeled as nonlinear stochastic dynamics, thus rejecting the hypothesis of low dimensional chaotic behavior. The ambient noise data utilized in this study are of duration 60 s measured at South China Sea.

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Section: Scale Dependent Lyapunov Exponentmentioning

confidence: 99%

On the dynamics of ocean ambient noise: Two decades later

Siddagangaiah

Guo

et al. 2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…9 Nevertheless, none of these measures and tests are fully reliable and all of them suffer from severe limitations. [10][11][12][13][14][15][16] Moreover, experimental chaotic signals are unavoidably contaminated by noise, making the classification task even more difficult. These drawbacks motivate the search of new methods that can efficiently distinguish chaotic from stochastic time series.…”

Section: Introductionmentioning

confidence: 99%

Discriminating chaotic and stochastic dynamics through the permutation spectrum test

Kulp

Zunino

2014

Chaos: An Interdisciplinary Journal of Nonlinear Science

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In this paper, we propose a new heuristic symbolic tool for unveiling chaotic and stochastic dynamics: the permutation spectrum test. Several numerical examples allow us to confirm the usefulness of the introduced methodology. Indeed, we show that it is robust in situations in which other techniques fail (intermittent chaos, hyperchaotic dynamics, stochastic linear and nonlinear correlated dynamics, and deterministic non-chaotic noise-driven dynamics). We illustrate the applicability and reliability of this pragmatic method by examining real complex time series from diverse scientific fields. Taking into account that the proposed test has the advantages of being conceptually simple and computationally fast, we think that it can be of practical utility as an alternative test for determinism. The importance of distinguishing between periodic, chaotic, and stochastic dynamics from time series analysis is well-recognized for understanding the mechanisms that govern the regarded complex systems. In this work, we have introduced a conceptually simple and computationally fast symbolic visual test for discriminating chaotic and stochastic dynamics, called the permutation spectrum test. Because the symbolization is made by implementing the Bandt and Pompe methodology, all the advantages associated with this natural encoding (simplicity, extremely fast calculation, robustness, and invariance with respect to monotonous transformations) are inherited by the permutation spectrum test. We have shown that this pragmatic approach is robust in situations in which other tests fail. We have also confirmed its practical utility by examining several experimental and natural time series.

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“…This is why the issue of distinguishing chaos from noise has been considered a classic and difficult one [37][38][39]. To fundamentally solve the problem, one has no choice but to resort to multiscale approaches.…”

Section: Distinguishing Chaos From Noisementioning

confidence: 99%

Information Entropy As a Basic Building Block of Complexity Theory

Gao

Liu

Zhang

et al. 2013

Entropy

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What is information? What role does information entropy play in this information exploding age, especially in understanding emergent behaviors of complex systems? To answer these questions, we discuss the origin of information entropy, the difference between information entropy and thermodynamic entropy, the role of information entropy in complexity theories, including chaos theory and fractal theory, and speculate new fields in which information entropy may play important roles.

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Detecting low-dimensional chaos by the “noise titration” technique: Possible problems and remedies

Cited by 21 publications

References 62 publications

On the dynamics of ocean ambient noise: Two decades later

On the dynamics of ocean ambient noise: Two decades later

Discriminating chaotic and stochastic dynamics through the permutation spectrum test

Information Entropy As a Basic Building Block of Complexity Theory

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