Chaotic Calculation and Prediction on Volume Deformation of MgO Concrete Based on Lyapunov Exponent

2010 ◽  
Vol 34-35 ◽  
pp. 446-450
Author(s):  
Jun Wei Song ◽  
Xiao Ping Cai
Keyword(s):  
Time Series ◽  
Phase Space ◽  
Lyapunov Exponent ◽  
Interpolation Method ◽  
Phase Space Reconstruction ◽  
Near Neighbor ◽  
Largest Lyapunov Exponent ◽  
Volume Deformation ◽  
Measured Deformation ◽  
The Largest Lyapunov Exponent

For the measured deformation time series of concrete engineering, linear and nonlinear chaotic prediction methods are represented for the autogenously volume deformation of concrete on basis of phase space reconstruction. Thus，the chaotic analytic method is set up for the prediction of the measured deformation time series of concrete engineering. At first，the autogenously volume deformation of RCC mixed with MgO are simply presented. Then，for the measured convergent deformation time series of RCC mixed with MgO，the interpolation method is adopted and an equal interval deformation time series is obtained. The results show that the largest Lyapunov exponent is 0.02 based on phase space reconstruction. Finally，it is separately predicted by the method of equidistance in near neighbor and that of the largest Lyapunov exponent prediction，and the predicted deformation values are ideal compared with the measured deformation values.

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.

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.

DETECTING THE STATE OF THE DUFFING OSCILLATOR BY PHASE SPACE TRAJECTORY AUTOCORRELATION

2013 ◽  
Vol 23 (04) ◽  
pp. 1350065 ◽  
Author(s):  
VAHID RASHTCHI ◽  
MOHSEN NOURAZAR
Keyword(s):  
Phase Space ◽  
Lyapunov Exponent ◽  
Duffing Oscillator ◽  
Simple Calculation ◽  
The State ◽  
Detection Methods ◽  
Largest Lyapunov Exponent ◽  
Chaotic Oscillator ◽  
The Largest Lyapunov Exponent ◽  
Phase Space Trajectory

Detecting the state of the Duffing oscillator, a type of well-known chaotic oscillator, deeply affects the accuracy of its application. Considering this, the present paper introduced a novel method for detecting the state of the Duffing oscillator. Binary outputs, simple calculation, high precision and fast response time were the main advantages of the phase space trajectory autocorrelation. Also, this study explained the largest Lyapunov exponent as well as a number of other methods commonly employed in detecting the state of the Duffing oscillator. The precision and effectiveness of the method introduced was compared with other well-known state detection methods such as the 0-1 test and the largest Lyapunov exponent.

ON THE COMPUTATION OF LYAPUNOV EXPONENTS FOR DISCRETE TIME SERIES: APPLICATIONS TO TWO-DIMENSIONAL SYMPLECTIC AND DISSIPATIVE MAPPINGS

2000 ◽  
Vol 10 (12) ◽  
pp. 2791-2805 ◽  
Author(s):  
ELENA LEGA ◽  
GABRIELLA DELLA PENNA ◽  
CLAUDE FROESCHLÉ ◽  
ALESSANDRA CELLETTI
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Discrete Series ◽  
Dissipative Systems ◽  
Data Series ◽  
Largest Lyapunov Exponent ◽  
Two Dimensional ◽  
Chaotic Motions ◽  
Conservative Systems ◽  
The Largest Lyapunov Exponent

Many techniques have been developed for the measure of the largest Lyapunov exponent of experimental short data series. The main idea, underlying the most common algorithms, is to mimic the method of computation proposed by Benettin and Galgani [1979]. The aim of the present paper is to provide an explanation for the reliability of some algorithms developed for short time series. To this end, we consider two-dimensional mappings as model problems and we compare the results obtained using the Benettin and Galgani method to those obtained using some algorithms for the computation of the largest Lyapunov exponent when dealing with short data series. In particular we focus our attention on conservative systems, which are not widely investigated in the literature. We show that using standard techniques the results obtained for discrete series related to area-preserving mappings are often unreliable, while dissipative systems are easier to analyze. In order to overcome the problem arising with conservative systems, we develop an alternative method, which takes advantage of the existing techniques. In particular, all algorithms provide a good approximation of the largest Lyapunov exponent in the strong chaotic symplectic case and in the dissipative one. However, the application of standard algorithms provides results which are not in agreement with the theoretical expectation for weak chaotic motions, and sometimes also for regular orbits. On the contrary, the method that we propose in this paper seems to work well for the weak chaotic case. Because of the speed of computation, we suggest to use all algorithms to cross-check the results.

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