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

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.

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