scholarly journals Predication of multivariable chaotic time series based on maximal Lyapunov exponent

2009 ◽  
Vol 58 (2) ◽  
pp. 756 ◽  
Author(s):  
Zhang Yong ◽  
Guan Wei
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Chaotic Time Series ◽  
Maximal Lyapunov Exponent

The Lyapunov Exponent Variance of an Electronic Manufacturing Enterprise’s Daily Qualified Rate Time Series by Improved Small Data Sets Approach

2012 ◽  
Vol 197 ◽  
pp. 271-277
Author(s):  
Zhu Ping Gong
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Chaotic Time Series ◽  
Quality System ◽  
Quality Level ◽  
Largest Lyapunov Exponent ◽  
Small Data ◽  
Data Set ◽  
Electronic Manufacturing ◽  
Small Data Set

Small data set approach is used for the estimation of Largest Lyapunov Exponent (LLE). Primarily, the mean period drawback of Small data set was corrected. On this base, the LLEs of daily qualified rate time series of HZ, an electronic manufacturing enterprise, were estimated and all positive LLEs were taken which indicate that this time series is a chaotic time series and the corresponding produce process is a chaotic process. The variance of the LLEs revealed the struggle between the divergence nature of quality system and quality control effort. LLEs showed sharp increase in getting worse quality level coincide with the company shutdown. HZ’s daily qualified rate, a chaotic time series, shows us the predictable nature of quality system in a short-run.

Design of fuzzy iterators to generate chaotic time series with assigned Lyapunov exponent

1996 ◽  
Vol 32 (4) ◽  
pp. 292 ◽  
Author(s):  
S. Baglio ◽  
L. Fortuna ◽  
G. Manganaro
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Chaotic Time Series

A robust method to estimate the maximal Lyapunov exponent of a time series

1994 ◽  
Vol 185 (1) ◽  
pp. 77-87 ◽  
Author(s):  
Holger Kantz
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Maximal Lyapunov Exponent ◽  
Robust Method

scholarly journals Noise-level estimation of noisy chaotic time series based on the invariant of the largest Lyapunov exponent

2012 ◽  
Vol 61 (6) ◽  
pp. 060503
Author(s):  
Yao Tian-Liang ◽  
Liu Hai-Feng ◽  
Xu Jian-Liang ◽  
Li Wei-Feng
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Noise Level ◽  
Chaotic Time Series ◽  
Largest Lyapunov Exponent ◽  
Noise Level Estimation ◽  
The Largest Lyapunov Exponent

Local Piecewise-Linearity Prediction Method of Chaotic Time Series

2013 ◽  
Vol 712-715 ◽  
pp. 2415-2418
Author(s):  
Juan Liu ◽  
Xue Wei Bai ◽  
Dao Cai Chi
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Prediction Method ◽  
Chaotic Time Series ◽  
Local Region ◽  
Liaoning Province ◽  
Largest Lyapunov Exponent ◽  
Region Method ◽  
Local Prediction ◽  
Piecewise Linearity

A Local Piecewise-Linearity Prediction method is presented, Based on the advantages and limitations of local prediction of chaotic time series. Taking time series of rainfall as example for prediction the rainfall of one city in Liaoning province, which includes the application of the largest Lyapunov exponent, Local-region method and Local Piecewise-Linearity method. The method proposed is proved practical in comparison with the observed data.

Chaoticity analysis of the current through pure, hydrogenated and hydrophobically modified PEG-Si thin films under varying relative humidity

Open Physics ◽  
2009 ◽  
Vol 7 (3) ◽  
Author(s):  
Kaan Atak ◽  
Ozgur Aybar ◽  
Gokhan Şahin ◽  
Avadis Hacınlıyan ◽  
Yani Skarlatos
Keyword(s):  
Thin Films ◽  
Time Series ◽  
Polyethylene Glycol ◽  
Lyapunov Exponent ◽  
Relative Humidity ◽  
Time Series Analysis ◽  
Maximal Lyapunov Exponent ◽  
Series Analysis ◽  
Hydrophobically Modified ◽  
Irregular Behavior

AbstractPolyethylene Glycol has an irregular current characteristic under constant voltage and slowly varying relative humidity. The current through a thin film of Gamma-isocyanatopropyltriethoxysilane added Polyethylene glycol (PEG-Si), its hydrogenated and hydrophobically modified forms, as a function of increasing relative humidity at equal time steps is analyzed for chaoticity. We suggest that the irregular behavior of current through PEG-Si thin films as a function of increasing relative humidity could best be analyzed for chaoticity using both time series analysis and detrended uctuation analysis; the relative humidity is kept as a slowly varying parameter. The presence of more then one regime is suggested by the calculation of the maximal Lyapunov exponents. Furthermore, the maximal Lyapunov exponent in each of the regimes was positive, thus confirming the presence of low dimensional chaos. DFA also confirms the presence of at least two different regimes, in agreement with the behavior of the maximal Lyapunov exponent in the time series analysis. We also suggest that the irregular behavior of the current through PEG-Si can be reduced by hydrogenating and hydrophobically modifying PEG-Si and the improvement in stability can be confirmed by our study.

OPTIMAL RECONSTRUCTION SPACE FOR ESTIMATING CORRELATION DIMENSION

1996 ◽  
Vol 06 (02) ◽  
pp. 377-381 ◽  
Author(s):  
ROBERT C. HILBORN ◽  
MINGZHOU DING
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Correlation Dimension ◽  
Chaotic Time Series ◽  
Largest Lyapunov Exponent ◽  
Correlation Integral ◽  
Past Work ◽  
Optimal Reconstruction ◽  
Scaling Region ◽  
Delay Coordinates

In this paper we consider the estimation of the correlation dimension from a scalar chaotic time series using delay coordinates. Past work has shown that there appears to be a reconstruction space for which the correlation integral has the longest scaling region. We give a firmer foundation to this idea by developing a theory that estimates the dimension of this “optimal” reconstruction space in terms of dynamical quantities such as the largest Lyapunov exponent.

Estimating the largest Lyapunov exponent and noise level from chaotic time series

2012 ◽  
Vol 22 (3) ◽  
pp. 033102 ◽  
Author(s):  
Tian-Liang Yao ◽  
Hai-Feng Liu ◽  
Jian-Liang Xu ◽  
Wei-Feng Li
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Noise Level ◽  
Chaotic Time Series ◽  
Largest Lyapunov Exponent ◽  
The Largest Lyapunov Exponent

scholarly journals Parallel kd-Tree Based Approach for Computing the Prediction Horizon Using Wolf’s Method

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
J. J. Águila ◽  
E. Arias ◽  
M. M. Artigao ◽  
J. J. Miralles
Keyword(s):  
Dynamical System ◽  
Time Series ◽  
Lyapunov Exponent ◽  
Measurement Data ◽  
Original System ◽  
Model Parameters ◽  
Maximal Lyapunov Exponent ◽  
Science And Engineering ◽  
Prediction Horizon ◽  
Means Of Measurement

In different fields of science and engineering, a model of a given underlying dynamical system can be obtained by means of measurement data records called time series. This model becomes very important to understand the original system behaviour and to predict the future values of that system. From the model, parameters such as the prediction horizon can be computed to obtain the point where the prediction becomes useless. In this work, a new parallel kd-tree based approach for computing the prediction horizon is presented. The parallel approach uses the maximal Lyapunov exponent, which is computed by Wolf’s method, as an estimator of the prediction horizon.

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