REDUCTION ENTROPY

1995 ◽  
Vol 05 (02) ◽  
pp. 585-593 ◽  
Author(s):  
FLORIS TAKENS
Keyword(s):  
Time Series ◽  
Dynamical Systems ◽  
Lyapunov Exponents ◽  
Numerical Determination ◽  
Sensitive Dependence ◽  
Noisy Time Series

In this paper we study the numerical determination of the different reduction entropies (or α-entropies) of dynamical systems from time series. This method is advocated as a more suitable way to investigate the different aspects of sensitive dependence on initial positions than the determination of Lyapunov exponents, especially in the case of “noisy” time series.

scholarly journals Evaluating Noise Sensitivity on the Time Series Determination of Lyapunov Exponents Applied to the Nonlinear Pendulum

2003 ◽  
Vol 10 (1) ◽  
pp. 37-50 ◽  
Author(s):  
L.F.P. Franca ◽  
M.A. Savi
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Time Series ◽  
Lyapunov Exponents ◽  
Random Noise ◽  
Noise Sensitivity ◽  
Correct Identification ◽  
Chaotic Motions ◽  
Nonlinear Pendulum

This contribution presents an investigation on noise sensitivity of some of the most disseminated techniques employed to estimate Lyapunov exponents from time series. Since noise contamination is unavoidable in cases of data acquisition, it is important to recognize techniques that could be employed for a correct identification of chaos. State space reconstruction and the determination of Lyapunov exponents are carried out to investigate the response of a nonlinear pendulum. Signals are generated by numerical integration of the mathematical model, selecting a single variable of the system as a time series. In order to simulate experimental data sets, a random noise is introduced in the signal. Basically, the analyses of periodic and chaotic motions are carried out. Results obtained from mathematical model are compared with the one obtained from time series analysis, evaluating noise sensitivity. This procedure allows the identification of the best techniques to be employed in the analysis of experimental data.

How to extract Lyapunov exponents from short and noisy time series

1997 ◽  
Vol 45 (5) ◽  
pp. 1378-1382 ◽  
Author(s):  
M. Banbrook ◽  
G. Ushaw ◽  
S. McLaughlin
Keyword(s):  
Time Series ◽  
Lyapunov Exponents ◽  
Noisy Time Series

scholarly journals Searching for determinism in observed data: a review of the issues involved

1994 ◽  
Vol 1 (1) ◽  
pp. 12-25 ◽  
Author(s):  
A. A. Tsonis ◽  
G. N. Triantafyllou ◽  
J. B. Elsner
Keyword(s):  
Time Series ◽  
Dynamical Systems ◽  
Lyapunov Exponents ◽  
Nonlinear Prediction

Abstract. In this paper we present a review of advances made and problems still existing in the application of the theory of chaos and dynamical systems to time series. In particular we discuss issues pertaining the estimation of dimensions, Lyapunov exponents and nonlinear prediction from an observable. We analyze the problems and discuss proper ways to deal with them.

PARAMETER SELECTION FOR PERMUTATION ENTROPY MEASUREMENTS

2007 ◽  
Vol 17 (10) ◽  
pp. 3729-3733 ◽  
Author(s):  
MATTHÄUS STANIEK ◽  
KLAUS LEHNERTZ
Keyword(s):  
Time Series ◽  
Dynamical Systems ◽  
Epileptic Seizures ◽  
Parameter Selection ◽  
Model Systems ◽  
Permutation Entropy ◽  
Epilepsy Patient ◽  
Synchronization Index ◽  
Noisy Time Series ◽  
Selection For

We investigate the applicability of the permutation entropy H and a synchronization index γ that is based on the changing tendency of temporal permutation entropies to analyze noisy time series from nonstationary dynamical systems with poorly understood properties. Using model systems, we first study the interdependencies of parameters involved in the calculation of both measures. Having identified appropriate parameter settings we then analyze long-lasting EEG time series recorded from an epilepsy patient. Our findings indicate that γ could be of interest for studies on the predictability of epileptic seizures.

scholarly journals QUANTIFYING SENSITIVE DEPENDENCE OF INITIAL CONDITION USING STRUCTURAL EQUATION MODELING

2019 ◽  
Vol 3 (Supplement_1) ◽  
pp. S377-S377
Author(s):  
Robert Moulder ◽  
Steve Boker
Keyword(s):  
Time Series ◽  
Structural Equation Modeling ◽  
Lyapunov Exponents ◽  
Structural Equation ◽  
Equation Modeling ◽  
Maximum Lyapunov Exponent ◽  
Initial Condition ◽  
Estimation Errors ◽  
Sensitive Dependence ◽  
Maximum Lyapunov Exponents

Abstract Human systems display sensitive dependence of initial condition. That is, even though two individuals may be similar in most regards, small differences between these individuals may have far reaching consequences later in life. In dynamical systems analysis, this sort of behavior is quantified with maximum Lyapunov exponents. These exponents quantify the degree to which small differences in initial condition between two systems affect trajectories of these systems later in time. Current methods for estimating maximum Lyapunov exponents are sensitive to noise and this sensitivity leads to estimation errors when researchers attempt to estimate these exponents on data obtained from human participants. Additionally, most current methods only allow for maximum Lyapunov exponent estimation using univariate time series. In this presentation, we present a method for using structural equation modeling for estimating latent maximum Lyapunov exponents from noisy multivariate time series and discuss applications of this method for analyzing human generated data.

Sign in / Sign up

Export Citation Format

Share Document