2012
DOI: 10.1016/j.chaos.2011.12.004
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Detecting low-dimensional chaos by the “noise titration” technique: Possible problems and remedies

Abstract: a b s t r a c tDistinguishing low-dimensional chaos from noise is an important issue in time series analysis. Among the many methods proposed for this purpose is the noise titration technique, which quantifies the amount of noise that needs to be added to the signal to fully destroy its nonlinearity. Two groups of researchers recently have questioned the validity of the technique. In this paper, we report a broad range of situations where the noise titration technique fails, and offer solutions to fix the prob… Show more

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Cited by 21 publications
(25 citation 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%
“…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%
“…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%
“…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%