scholarly journals Exponential separation and principal Lyapunov exponent/spectrum for random/nonautonomous parabolic equations

2003 ◽  
Vol 191 (1) ◽  
pp. 175-205 ◽  
Author(s):  
Janusz Mierczyński ◽  
Wenxian Shen
Keyword(s):  
Lyapunov Exponent ◽  
Parabolic Equations ◽  
Exponential Separation ◽  
Lyapunov Exponent Spectrum

Study on State Recognition of ASCE Benchmark Based on Lyapunov Exponent Spectrum Entropy

2011 ◽  
Vol 243-249 ◽  
pp. 5435-5439 ◽  
Author(s):  
Jian Xi Yang ◽  
Jian Ting Zhou ◽  
Yue Chen
Keyword(s):  
Lyapunov Exponent ◽  
Time Sequence ◽  
Maximum Lyapunov Exponent ◽  
Entropy Analysis ◽  
Structural System ◽  
Time Duration ◽  
State Recognition ◽  
Chaotic Characteristic ◽  
Lyapunov Exponent Spectrum ◽  
Maximum Lyapunov Exponents

The paper has made a maximum Lyapunov exponent and Lyapunov exponent spectrum entropy analysis of ASCE Benchmark using non-linear theory and chaos time sequence. The maximum Lyapunov exponents in the two kinds of structural monitored data are both over zero, indicating that in the structural system chaos phenomenon has appeared. And, experiments have shown that the maximum Lyapunov exponent is sensitive of the amount of samples and the time delay. So, to compute the chaos index, the amount of samples and the time duration are of importance. Meanwhile, the Lyapunov exponent spectrum entropy is effective to measure the chaotic characteristic of the system, but ,the entropy is less sensitive to state recognition more than the max Lyapunov exponent.

Dynamics of Human Spine in Jumps Using Lyapunov Exponents

2009 ◽  
Author(s):  
Eliza A. Banu ◽  
Dan Marghitu ◽  
P. K. Raju
Keyword(s):  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Largest Lyapunov Exponent ◽  
Kinematic Data ◽  
Finite Time Lyapunov Exponents ◽  
Human Spine ◽  
Chaotic Nature ◽  
Male Subjects ◽  
Lyapunov Exponent Spectrum

Characterizing and quantifying the local dynamics of the human spine during various athletic exercises is important for therapeutic and physiotherapy reasons or athletic related effects on the human spine. In this study we computed the largest finite-time Lyapunov exponents for the spine of a human subject during an athletic exercise for several volunteers. The kinematic data was collected using the 3D motion capture system (Motion Realty Inc.). Four healthy male subjects were asked to perform two sets of 30 jumps. In order to draw a conclusion about the chaotic nature of the dynamics of the lumbar spine Lyapunov exponent spectrum was calculated for each volunteer which included four Lyapunov exponents, one negative, one very close to zero and two positive. Subjects 1, 2 and 4 registered a significant increase in the largest Lyapunov exponent from the first set jumps to the next. Subject 3 registered no change in the values of Lyapunov exponents. Nonlinear analysis of the human spine demonstrates the chaotic nature of the system. The computation of the largest Lyapunov exponents enables a more precise characterization of the dynamics of the human spine.

Estimation of a Lyapunov-exponent spectrum of plasma chaos

1994 ◽  
Vol 50 (2) ◽  
pp. 1062-1069 ◽  
Author(s):  
W. Huang ◽  
W. X. Ding ◽  
D. L. Feng ◽  
C. X. Yu
Keyword(s):  
Lyapunov Exponent ◽  
Lyapunov Exponent Spectrum

HYPERCHAOS Qi SYSTEM

2010 ◽  
Vol 24 (24) ◽  
pp. 4771-4778 ◽  
Author(s):  
XING-YUAN WANG ◽  
YONG-FENG GAO ◽  
YAO-XIAN ZHANG
Keyword(s):  
Phase Diagram ◽  
Lyapunov Exponent ◽  
Numerical Simulations ◽  
Bifurcation Diagram ◽  
Nonlinear Term ◽  
Linear Term ◽  
Nonlinear Controller ◽  
Chaos System ◽  
Lyapunov Exponent Spectrum

This paper presents a four-dimensional hyperchaos Qi system, obtained by adding linear term and nonlinear term of nonlinear controller to Qi chaos system. The hyperchaos Qi system is studied by bifurcation diagram, Lyapunov exponent spectrum and phase diagram. Numerical simulations show that the new system's behavior can be periodic, chaotic and hyperchaotic as the parameter varies.

EXTRACTING LYAPUNOV EXPONENTS FROM SHORT TIME SERIES OF LOW PRECISION

1992 ◽  
Vol 06 (02) ◽  
pp. 55-75 ◽  
Author(s):  
X. ZENG ◽  
R.A. PIELKE ◽  
R. EYKHOLT
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Polynomial Approximation ◽  
Qr Decomposition ◽  
Short Time Series ◽  
Order Polynomial ◽  
Free Parameters ◽  
Short Time ◽  
Lyapunov Exponent Spectrum

Different methods for computing the Lyapunov-exponent spectrum from a time series are reviewed. All algorithms are based on either Gram-Schmidt orthonormalization or Householder QR decomposition, and they use either the linearized map or a higher-order polynomial approximation. They also differ in implementation details. The ability to use these methods for a short time series of low precision is investigated, with special attention being given to the practicality of these algorithms; i.e., their efficiency and accuracy and the number of adjustable free parameters.

Generating Multiple Chaotic Attractors from Sprott B System

2016 ◽  
Vol 26 (11) ◽  
pp. 1650177 ◽  
Author(s):  
Qiang Lai ◽  
Shiming Chen
Keyword(s):  
Lyapunov Exponent ◽  
Function Method ◽  
Polynomial Function ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Nonlinear Phenomenon ◽  
Bifurcation Diagrams ◽  
Initial Values ◽  
Index 2 ◽  
Lyapunov Exponent Spectrum

Multiple chaotic attractors, implying several independent chaotic attractors generated simultaneously in a system from different initial values, are a very interesting and important nonlinear phenomenon, but there are few studies that have previously addressed it to our best knowledge. In this paper, we propose a polynomial function method for generating multiple chaotic attractors from the Sprott B system. The polynomial function extends the number of index-2 saddle foci, which determines the emergence of multiple chaotic attractors in the system. The analysis of the equilibria is presented. Two coexisting chaotic attractors, three coexisting chaotic attractors and four coexisting chaotic attractors are investigated for verifying the effectiveness of the method. The chaotic characteristics of the attractors are shown by bifurcation diagrams, Lyapunov exponent spectrum and phase portraits.

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