scholarly journals On the maximum Lyapunov exponent of the motion in a chaotic layer

JETP Letters ◽  
2004 ◽  
Vol 79 (11) ◽  
pp. 523-528 ◽  
Author(s):  
I. I. Shevchenko
Keyword(s):  
Lyapunov Exponent ◽  
Maximum Lyapunov Exponent

Non-Linearity and Chaotic Behaviour in Cyprus Stock Market

2015 ◽  
Vol 5 (4) ◽  
Author(s):  
Athina Bougioukou
Keyword(s):  
Lyapunov Exponent ◽  
Stock Market ◽  
Chaos Theory ◽  
Linear Dependence ◽  
Chaotic Behavior ◽  
Efficient Market Hypothesis ◽  
Chaotic Behaviour ◽  
Maximum Lyapunov Exponent ◽  
Efficient Market ◽  
General Index

The intention of this research is to investigate the aspect of non-linearity and chaotic behavior of the Cyprus stock market. For this purpose, we use non-linearity and chaos theory. We perform BDS, Hinich-Bispectral tests and compute Lyapunov exponent of the Cyprus General index. The results show that existence of non-linear dependence and chaotic features as the maximum Lyapunov exponent was found to be positive. This study is important because chaos and efficient market hypothesis are mutually exclusive aspects. The efficient market hypothesis which requires returns to be independent and identically distributed (i.i.d.) cannot be accepted.

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.

scholarly journals An investigation of EEG dynamics in an animal model of temporal lobe epilepsy using the maximum Lyapunov exponent

2009 ◽  
Vol 216 (1) ◽  
pp. 115-121 ◽  
Author(s):  
Sandeep P. Nair ◽  
Deng-Shan Shiau ◽  
Jose C. Principe ◽  
Leonidas D. Iasemidis ◽  
Panos M. Pardalos ◽  
...  
Keyword(s):  
Animal Model ◽  
Lyapunov Exponent ◽  
Temporal Lobe Epilepsy ◽  
Temporal Lobe ◽  
Maximum Lyapunov Exponent

Chaotic Dynamics of Piezoelectric MEMS Based on Maximum Lyapunov Exponent and Smaller Alignment Index Computations

2020 ◽  
Vol 30 (09) ◽  
pp. 2030025
Author(s):  
M. V. Tchakui ◽  
P. Woafo ◽  
Ch. Skokos
Keyword(s):  
Lyapunov Exponent ◽  
Chaotic Dynamics ◽  
Detection Method ◽  
Dynamical Behavior ◽  
Time Dependent ◽  
Maximum Lyapunov Exponent ◽  
Nonconservative System ◽  
Surface Of Section ◽  
Chaos Detection ◽  
Piezoelectric Mems

We characterize the dynamical states of a piezoelectric micrcoelectromechanical system (MEMS) using several numerical quantifiers including the maximum Lyapunov exponent, the Poincaré Surface of Section and a chaos detection method called the Smaller Alignment Index (SALI). The analysis makes use of the MEMS Hamiltonian. We start our study by considering the case of a conservative piezoelectric MEMS model and describe the behavior of some representative phase space orbits of the system. We show that the dynamics of the piezoelectric MEMS becomes considerably more complex as the natural frequency of the system’s mechanical part decreases. This refers to the reduction of the stiffness of the piezoelectric transducer. Then, taking into account the effects of damping and time-dependent forces on the piezoelectric MEMS, we derive the corresponding nonautonomous Hamiltonian and investigate its dynamical behavior. We find that the nonconservative system exhibits a rich dynamics, which is strongly influenced by the values of the parameters that govern the piezoelectric MEMS energy gain and loss. Our results provide further evidences of the ability of the SALI to efficiently characterize the chaoticity of dynamical systems.

Very short-term maximum Lyapunov exponent forecasting tool for distributed photovoltaic output

2018 ◽  
Vol 229 ◽  
pp. 1128-1139 ◽  
Author(s):  
Lingwei Zheng ◽  
Zhaokun Liu ◽  
Junnan Shen ◽  
Chenxi Wu
Keyword(s):  
Lyapunov Exponent ◽  
Maximum Lyapunov Exponent ◽  
Short Term

Subharmonic and Chaotic Motions of a Hybrid Squeeze-Film Damper-Mounted Rigid Rotor With Active Control

2002 ◽  
Vol 124 (2) ◽  
pp. 198-208 ◽  
Author(s):  
Chieh-Li Chen ◽  
Her-Terng Yau ◽  
Yunhua Li
Keyword(s):  
Lyapunov Exponent ◽  
Active Control ◽  
Chaotic Motion ◽  
Numerical Results ◽  
Operating Conditions ◽  
Squeeze Film ◽  
Speed Ratio ◽  
Maximum Lyapunov Exponent ◽  
Rigid Rotor ◽  
Squeeze Film Damper

The hybrid squeeze-film damper bearing with active control is proposed in this paper. The pressure distribution and the dynamics of a rigid rotor supported by such bearing are studied. A PD (proportional-plus-derivative) controller is used to stabilize the rotor-bearing system. Numerical results show that, due to the nonlinear factors of oil film force, the trajectory of the rotor demonstrates a complex dynamics with rotational speed ratio s. Poincare´ maps, bifurcation diagrams, and power spectra are used to analyze the behavior of the rotor trajectory in the horizontal and vertical directions under different operating conditions. The maximum Lyapunov exponent and fractal dimension concepts are used to determine if the system is in a state of chaotic motion. Numerical results show that the maximum Lyapunov exponent of this system is positive and the dimension of the rotor trajectory is fractal at the nondimensional speed ratio s=3.0, which indicate that the rotor trajectory is chaotic under such operation condition. In order to avoid the nonsynchronous chaotic vibrations, an increased proportional gain is applied to control this system. It is shown that the rotor trajectory will leave chaotic motion to periodic motion in the steady state under control action.

The Meridional Pressure Gradient Prediction by the Global Climate Model

2017 ◽  
Vol 866 ◽  
pp. 164-167
Author(s):  
Sunisa Saiuparad
Keyword(s):  
Lyapunov Exponent ◽  
Pressure Gradient ◽  
Climate Model ◽  
Global Climate ◽  
Global Climate Model ◽  
Finite Size ◽  
Maximum Lyapunov Exponent ◽  
Northeast Monsoon ◽  
Version 2.0 ◽  
Pressure Changes

The pressure gradient is a physical quantity that describes in which direction and at what rate the pressure changes the most rapidly around a particular location. The meridional pressure gradient can be prediction for the main forces acting on the air to make it move as wind. The randomly selected cases for this experiment are the Asian northeast monsoon downscaling for December 2049. The global climate model is the Bjerknes Centre for Climate Research (BCCR), University of Bergen, Norway. Bergen Climate Model (BCM) Version 2.0 (BCCR-BCM2.0). The data predictions are the A2 scenario and COMMIT scenario. In this research maximum Lyapunov exponent (MLE) and finite size Lyapunov exponent (FSLE) for every 24-hr interval of the meridional pressure gradient from the BCCR-BCM2.0 model are calculated. The results show that the meridional pressure gradient prediction by the BCCR-BCM2.0 is not sensitive to scenario.

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