Deterministic chaos and the first positive Lyapunov exponent: a nonlinear analysis of the human electroencephalogram during sleep

1993 ◽  
Vol 69 (2) ◽  
pp. 139-146 ◽  
Author(s):  
J. Fell ◽  
J. Röschke ◽  
P. Beckmann
Keyword(s):  
Lyapunov Exponent ◽  
Nonlinear Analysis ◽  
Deterministic Chaos ◽  
Positive Lyapunov Exponent ◽  
Human Electroencephalogram

scholarly journals Chaotic dynamics in Parkfield region, California and characteristics earthquakes

MAUSAM ◽  
2021 ◽  
Vol 50 (1) ◽  
pp. 99-104
Author(s):  
H. N. SRIVASTAVA ◽  
K. C. SINHA RAY
Keyword(s):  
Lyapunov Exponent ◽  
Chaotic Dynamics ◽  
Initial Conditions ◽  
Strong Dependence ◽  
Plate Boundary ◽  
Deterministic Chaos ◽  
Himalayan Region ◽  
Positive Lyapunov Exponent ◽  
Collision Type ◽  
Earthquake Predictability

Based on about 75000 earthquakes in the California region detected through Parkfield network during the years 1969-1987, the occurrence of chaos was examined by two different approaches, namely, strange at tractor dimension and the Lyapunov exponent. The strange at tractor dimension was found as 6.3 in this region suggesting atleast 7 parameters for earthquake predictability. Small positive Lyapunov exponent of 0.045 provided further evidence for deterministic chaos in the region which showed strong dependence on the initial conditions. Implications of chaotic dynamics on characteristic Parkfield earthquakes has been discussed. The strange at tractor dimension in the region could be representative for the Transform type of plate boundary which is lower than that reported for continent collision type of plate boundary which is lower than that reported for continent collision type of plate boundary near Hindukush northwest Himalayan region.

On maximizing the positive Lyapunov exponent of chaotic oscillators applying DE and PSO

2019 ◽  
Vol 7 (4) ◽  
pp. 1157-1172 ◽  
Author(s):  
Alejandro Silva-Juárez ◽  
Carlos Javier Morales-Pérez ◽  
Luis Gerardo de la Fraga ◽  
Esteban Tlelo-Cuautle ◽  
José de Jesús Rangel-Magdaleno
Keyword(s):  
Lyapunov Exponent ◽  
Positive Lyapunov Exponent ◽  
Chaotic Oscillators

scholarly journals A relation between Lyapunov exponents, Hausdorff dimension and entropy

1981 ◽  
Vol 1 (4) ◽  
pp. 451-459 ◽  
Author(s):  
Anthony Manning
Keyword(s):  
Lyapunov Exponent ◽  
Hausdorff Dimension ◽  
Invariant Measure ◽  
Lyapunov Exponents ◽  
Unstable Manifold ◽  
Positive Lyapunov Exponent ◽  
Axiom A ◽  
Generic Points

AbstractFor an Axiom A diffeomorphism of a surface with an ergodic invariant measure we prove that the entropy is the product of the positive Lyapunov exponent and the Hausdorff dimension of the set of generic points in an unstable manifold.

CHARACTERIZATION OF CHAOTICITY IN THE TRANSIENT CURRENT THROUGH PMMA THIN FILMS

Fractals ◽  
2006 ◽  
Vol 14 (02) ◽  
pp. 125-131 ◽  
Author(s):  
A. HACINLIYAN ◽  
Y. SKARLATOS ◽  
H. A. YILDIRIM ◽  
G. SAHIN
Keyword(s):  
Thin Films ◽  
Time Series ◽  
Lyapunov Exponent ◽  
Power Law ◽  
Chaotic Behavior ◽  
Transient Current ◽  
Positive Lyapunov Exponent ◽  
Aluminum Films ◽  
Thin Aluminum

Chaotic behavior in the transient current through thin Aluminum-PMMA-Aluminum films has been analyzed for times ranging up to 30,000s, in the temperature range 293–363K for applied voltages in the range 10–80V. Time series analysis reveals a positive Lyapunov exponent consistently and reproducibly throughout this range. Power law relaxation as reflected by the autocorrelation function and the positive Lyapunov exponent show parallel behaviors as a function of applied electric field.

scholarly journals The Study of the Chaotic Behavior in Retailer's Demand Model

2008 ◽  
Vol 2008 ◽  
pp. 1-12 ◽  
Author(s):  
Junhai Ma ◽  
Yun Feng
Keyword(s):  
Lyapunov Exponent ◽  
Systems Theory ◽  
Bifurcation Diagram ◽  
Chaotic Systems ◽  
Chaotic Behavior ◽  
Deterministic Chaos ◽  
Model Parameters ◽  
Initial Condition ◽  
Maximal Lyapunov Exponent ◽  
Demand Model

Based on the work of domestic and foreign scholars and the application of chaotic systems theory, this paper presents an investigation simulation of retailer's demand and stock. In simulation of the interaction, the behavior of the system exhibits deterministic chaos with consideration of system constraints. By the method of space's reconstruction, the maximal Lyapunov exponent of retailer's demand model was calculated. The result shows the model is chaotic. By the results of bifurcation diagram of model parameters , and changing initial condition, the system can be led to chaos.

scholarly journals COMBINING METHODS OF FREQUENCY FILTERING AND NONLINEAR ANALYSIS FOR SOMNOLOGICAL STUDY OF EEG SIGNALS

2016 ◽  
Vol 1 (3) ◽  
pp. 45-50
Author(s):  
O I Antipov ◽  
A V Zakharov
Keyword(s):  
Nonlinear Analysis ◽  
Classical Method ◽  
Deterministic Chaos ◽  
Entropy Method ◽  
Preliminary Treatment ◽  
Frequency Filtering ◽  
Eeg Signals ◽  
Recovery Method ◽  
Correlation Integral ◽  
Non Linear

Aim - combined use of frequency and nonlinear analysis methods for obtaining hypnograms by analyzing electroencephalographic (EEG) signals during somnological studies. Methods. Frequency filtering methods were used for preliminary treatment of EEG signals before the following nonlinear analysis. As non-linear methods of analysis we used fractal methods of deterministic chaos, such as Hurst’s method of the normalized amplitude, approximate entropy method, calculation of the correlation integral by Grassberger and Procaccia’s method. For the possibility of applying the last two methods we used quasi phase space recovery method according to the Taken’s theorem. As a result of non-linear analysis we obtained hypnograms reflecting the transition between the stages of sleep in patients undergoing somnological examination. To assess the reliability of the results, they were compared to the hypnograms obtained by the classical method based on the rules of Rehchaffen and Keyls. Also the problems associated with the occurrence of various types of interference were considered and methods for reducing their influence on the final results were suggested. Results. We can conclude that using these methods with appropriate selection of the parameters, employing the necessary normalization of raw data, and averaging the results allow us to obtain hypnogram having a full match of defined phases of sleep for about half of the periods recorded by EEG. To obtain these results it is sufficient to use only one channel of EEG recording.

Computation of the largest positive Lyapunov exponent using rounding mode and recursive least square algorithm

2018 ◽  
Vol 112 ◽  
pp. 36-43 ◽  
Author(s):  
Márcia L.C. Peixoto ◽  
Erivelton G. Nepomuceno ◽  
Samir A.M. Martins ◽  
Márcio J. Lacerda
Keyword(s):  
Lyapunov Exponent ◽  
Least Square ◽  
Positive Lyapunov Exponent ◽  
Recursive Least Square ◽  
Recursive Least Square Algorithm
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