Proper choice of the time delay for the analysis of chaotic time series

Liebert, Wolfgang; Schuster, H. G.

doi:10.1016/0375-9601(89)90169-2

Cited by 303 publications

(156 citation statements)

References 10 publications

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“…It must also be emphasized that the parameters used to reconstruct the attractor exert an important influence on the values of "traditional" nonlinear descriptors. This is the case for τ , that we defined as the delay needed to reach the first zero of an autocorrelation function (Liebert and Schuster, 1989) rather than arbitrarily . These constraints are alleviated by the noise titration approach.…”

Section: Technical Issuesmentioning

confidence: 99%

“…The analysis pertaining to a finite and noisy data set rather than to an infinite noise-free data set, it was not possible to choose the time delay arbitrarily. Indeed, under such conditions, the time delay influences the quality of the reconstructed trajectory and thereby the values of the characteristic quantities under consideration (Liebert and Schuster, 1989). Among the many available possibilities to determine an appropriate time delay, we chose to use the time to the first zero of an autocorrelation function as our time delay (Liebert and Schuster, 1989).…”

Section: Legends To the Figuresmentioning

confidence: 99%

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Chaotic dynamics of resting ventilatory flow in humans assessed through noise titration

Wysocki

Fiamma

Straus

et al. 2006

Respiratory Physiology & Neurobiology

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The mammalian ventilatory behaviour exhibits nonlinear dynamics as reflected by certain nonlinearity or complexity indicators (e.g. correlation dimension, approximate entropy, Lyapunov exponents...) but this is not sufficient to determine its possible chaotic nature. To address this, we applied the noise titration technique, previously shown to discern and quantify chaos in short and noisy time series, to ventilatory flow recordings obtained in quietly breathing normal humans. Nine subjects (8 men and 1 woman, 24-42 yrs) were studied during 15-minute epochs of ventilatory steadystate (10.1±3.0 breaths/minute, tidal volume 0.63±0.2L). Noise titration applied to the unfiltered signals subsampled at 5 Hz detected nonlinearity in all cases (noise limit 20.2±12.5%). Noise limit values were weakly correlated to the correlation dimension and the largest Lyapunov exponent of the signals. This study shows that the noise titration approach evidences a chaotic dimension to the behavior of ventilatory flow over time in normal humans during tidal breathing.

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Section: Technical Issuesmentioning

confidence: 99%

Section: Legends To the Figuresmentioning

confidence: 99%

Chaotic dynamics of resting ventilatory flow in humans assessed through noise titration

Wysocki

Fiamma

Straus

et al. 2006

Respiratory Physiology & Neurobiology

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“…The method of autocorrelation function was used for determination of τ as the delay causing the value of (1-1/e) its initial of the autocorrelation function [16]. The embedding dimensions m were estimated using the Grassberger-Procaccia algorithm method proposed by Grassberger [17,18], which is suitable for shorter time series.…”

Section: B Analysis Methods Of Chaos Characteristicsmentioning

confidence: 99%

Analysis on Phase Space Reconstruction and Chaotic Characteristic of Element Concentration Series of Gold Deposit

Wan¹,

Zhu²,

Deng³

2015

Advances in Intelligent Systems Research

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“…In [11] it is selected as the reciprocal of the highest relevant frequency of the time series. It is proposed in [12] to use the information dimension, which is a kind of fractal dimensions, as the time delay. However, one of the most reliable methods is presented by Fraser [13].…”

Section: Embedding Theory and Dynamic Reconstructionmentioning

confidence: 99%

Forecasting the Unknown Dynamics in NN3 Database Using a Nonlinear Autoregressive Recurrent Neural Network

Safavieh¹,

Andalib²,

Andalib³

2007

2007 International Joint Conference on Neural Networks

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Abstract-In this paper, a nonlinear autoregressive (NAR) recurrent neural network is used for the prediction of the next 18 data samples of each time series in a set of 11 unknown dynamics in NN3 Database. The models are built on the reconstructed state spaces of data and no other domain knowledge is available to be used. Here, we clarify that the employed method is in part similar to a superior subclass of recurrent neural network, namely the nonlinear autoregressive model with exogenous inputs (NARX). Using the extensive available research about NARX networks, we briefly explain that our model is preferred to the both non-recursive and even other recurrent predictors, because of its intrinsic ability for learning long term dependencies in time series. As the desired values of the predicted time series are not available yet, no analysis have been performed on the presented results.

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Proper choice of the time delay for the analysis of chaotic time series

Cited by 303 publications

References 10 publications

Chaotic dynamics of resting ventilatory flow in humans assessed through noise titration

Chaotic dynamics of resting ventilatory flow in humans assessed through noise titration

Analysis on Phase Space Reconstruction and Chaotic Characteristic of Element Concentration Series of Gold Deposit

Forecasting the Unknown Dynamics in NN3 Database Using a Nonlinear Autoregressive Recurrent Neural Network

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