scholarly journals Strategies for computation of Lyapunov exponents estimates from discrete data

2019 ◽  
Author(s):  
Cyril Fischer ◽  
Jiří Náprstek
Keyword(s):  
Lyapunov Exponents ◽  
Discrete Data

Integrated Fractional white Noise as an Alternative to Multifractional Brownian Motion

2007 ◽  
Vol 44 (02) ◽  
pp. 393-408 ◽  
Author(s):  
Allan Sly
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
White Noise ◽  
Gaussian Process ◽  
Discrete Data ◽  
Hölder Exponent ◽  
Scaling Properties ◽  
Multifractional Brownian Motion ◽  
Local Properties

Multifractional Brownian motion is a Gaussian process which has changing scaling properties generated by varying the local Hölder exponent. We show that multifractional Brownian motion is very sensitive to changes in the selected Hölder exponent and has extreme changes in magnitude. We suggest an alternative stochastic process, called integrated fractional white noise, which retains the important local properties but avoids the undesirable oscillations in magnitude. We also show how the Hölder exponent can be estimated locally from discrete data in this model.

Lyapunov Exponents

2016 ◽  
Author(s):  
Arkady Pikovsky ◽  
Antonio Politi
Keyword(s):  
Lyapunov Exponents

EFFECTS OF TREND AND PERIODICITY ON THE CORRELATION DIMENSION AND THE LYAPUNOV EXPONENTS

2008 ◽  
Vol 18 (12) ◽  
pp. 3679-3687 ◽  
Author(s):  
AYDIN A. CECEN ◽  
CAHIT ERKAL
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Correlation Dimension ◽  
Time Series Data ◽  
Logistic Map ◽  
Model Identification ◽  
Series Data ◽  
Largest Lyapunov Exponent ◽  
The Impact

We present a critical remark on the pitfalls of calculating the correlation dimension and the largest Lyapunov exponent from time series data when trend and periodicity exist. We consider a special case where a time series Zi can be expressed as the sum of two subsystems so that Zi = Xi + Yi and at least one of the subsystems is deterministic. We show that if the trend and periodicity are not properly removed, correlation dimension and Lyapunov exponent estimations yield misleading results, which can severely compromise the results of diagnostic tests and model identification. We also establish an analytic relationship between the largest Lyapunov exponents of the subsystems and that of the whole system. In addition, the impact of a periodic parameter perturbation on the Lyapunov exponent for the logistic map and the Lorenz system is discussed.

A two-dimensional sideways problem with random discrete data

2021 ◽  
Vol 86 ◽  
pp. 16-32
Author(s):  
Dang Duc Trong ◽  
Tran Quoc Viet ◽  
Vo Dang Khoa ◽  
Nguyen Thi Hong Nhung
Keyword(s):  
Discrete Data ◽  
Two Dimensional

scholarly journals Hyperchaotic Image Encryption Based on Multiple Bit Permutation and Diffusion

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 510
Author(s):  
Taiyong Li ◽  
Duzhong Zhang
Keyword(s):  
Big Data ◽  
Lyapunov Exponents ◽  
Image Encryption ◽  
Hyperchaotic System ◽  
Encryption Scheme ◽  
Image Content ◽  
Image Security ◽  
Level Data ◽  
Different Types ◽  
And Diffusion

Image security is a hot topic in the era of Internet and big data. Hyperchaotic image encryption, which can effectively prevent unauthorized users from accessing image content, has become more and more popular in the community of image security. In general, such approaches conduct encryption on pixel-level, bit-level, DNA-level data or their combinations, lacking diversity of processed data levels and limiting security. This paper proposes a novel hyperchaotic image encryption scheme via multiple bit permutation and diffusion, namely MBPD, to cope with this issue. Specifically, a four-dimensional hyperchaotic system with three positive Lyapunov exponents is firstly proposed. Second, a hyperchaotic sequence is generated from the proposed hyperchaotic system for consequent encryption operations. Third, multiple bit permutation and diffusion (permutation and/or diffusion can be conducted with 1–8 or more bits) determined by the hyperchaotic sequence is designed. Finally, the proposed MBPD is applied to image encryption. We conduct extensive experiments on a couple of public test images to validate the proposed MBPD. The results verify that the MBPD can effectively resist different types of attacks and has better performance than the compared popular encryption methods.

scholarly journals The Performance of Post-Fall Detection Using the Cross-Dataset: Feature Vectors, Classifiers and Processing Conditions

Sensors ◽  
2021 ◽  
Vol 21 (14) ◽  
pp. 4638
Author(s):  
Bummo Koo ◽  
Jongman Kim ◽  
Yejin Nam ◽  
Youngho Kim
Keyword(s):  
Time Series ◽  
Fall Detection ◽  
Discrete Data ◽  
Classification Performance ◽  
Training Data ◽  
Processing Conditions ◽  
Feature Vectors ◽  
External Data ◽  
Public Dataset ◽  
The Cross

In this study, algorithms to detect post-falls were evaluated using the cross-dataset according to feature vectors (time-series and discrete data), classifiers (ANN and SVM), and four different processing conditions (normalization, equalization, increase in the number of training data, and additional training with external data). Three-axis acceleration and angular velocity data were obtained from 30 healthy male subjects by attaching an IMU to the middle of the left and right anterior superior iliac spines (ASIS). Internal and external tests were performed using our lab dataset and SisFall public dataset, respectively. The results showed that ANN and SVM were suitable for the time-series and discrete data, respectively. The classification performance generally decreased, and thus, specific feature vectors from the raw data were necessary when untrained motions were tested using a public dataset. Normalization made SVM and ANN more and less effective, respectively. Equalization increased the sensitivity, even though it did not improve the overall performance. The increase in the number of training data also improved the classification performance. Machine learning was vulnerable to untrained motions, and data of various movements were needed for the training.

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