Symbolic diffusion entropy rate of chaotic time series as a surrogate measure for the largest Lyapunov exponent

2019 ◽  
Vol 100 (3) ◽  
Author(s):  
Kota Shiozawa ◽  
Takaya Miyano
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Chaotic Time Series ◽  
Entropy Rate ◽  
Largest Lyapunov Exponent ◽  
Diffusion Entropy ◽  
Surrogate Measure ◽  
The Largest 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.

CHAOTIC ANALYSIS OF A TIME SERIES COMPOSED OF SEISMIC EVENTS RECORDED IN JAPAN

1994 ◽  
Vol 04 (01) ◽  
pp. 87-98 ◽  
Author(s):  
G.P. PAVLOS ◽  
L. KARAKATSANIS ◽  
J.B. LATOUSSAKIS ◽  
D. DIALETIS ◽  
G. PAPAIOANNOU
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Initial Conditions ◽  
Low Frequency ◽  
Underlying Mechanism ◽  
Largest Lyapunov Exponent ◽  
Seismic Events ◽  
Earthquake Dynamics ◽  
The Largest Lyapunov Exponent ◽  
Low Dimensional

A chaotic analysis approach was applied to an earthquake time series recorded in the Japanese area in order to test the assumption that the earthquake process could be the manifestation of a chaotic low dimensional process. For the study of the seismicity we have used a time series consisting of time differences between two consecutive seismic events with magnitudes greater than 2.6. The results of our study show that the underlying mechanism, as expressed by the time series, can be described by low dimensional chaotic dynamics. The power spectrum of the time series shows a power law profile with two slopes, α=1.4 in the low frequency and α=0.05 in the high frequency regions, while the slopes of the correlation integrals show an apparent plateau at the scaling region, which saturates at the value D≈3.2. The largest Lyapunov exponent was found to be ≈0.9. The positive value of the largest Lyapunov exponent reveals strong sensitivity to initial conditions of the supposed earthquake dynamics.

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.

Quantifying Interactions in Nonlinear Feedback Dynamics: A Time Series Analysis

2019 ◽  
Vol 29 (01) ◽  
pp. 1950012
Author(s):  
Catherine Kyrtsou ◽  
Christina D. Mikropoulou
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Time Series Analysis ◽  
Largest Lyapunov Exponent ◽  
Nonlinear Feedback ◽  
System Complexity ◽  
Feedback Mechanisms ◽  
Series Analysis ◽  
The Largest Lyapunov Exponent

In this paper, we further study the dynamics of the Kyrtsou model composed of heterogeneous nonlinear feedback rules. For various levels and types of underlying nonlinearity, we analyze the resulting time series by means of the largest Lyapunov exponent. Our results highlight that the observed interaction among feedback mechanisms cannot lead to a univocal interpretation of system complexity.

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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