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

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.

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.

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.

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