ADVANCED COMPUTING TOPOLOGICAL AND DYNAMICAL INVARIANTS OF RELATIVISTIC BACKWARD-WAVE TUBE TIME SERIES IN CHAOTIC AND HYPERCHAOTIC REGIMES

The advanced results of computing the dynamical and topological invariants (correlation dimensions values, embedding, Kaplan-York dimensions, Lyapunov’s exponents, Kolmogorov entropy etc) of the dynamics time series of the relativistic backward-wave tube with accounting for dissipation and space charge field and other effects are presented for chaotic and hyperchaotic regimes. It is solved a system of equations for unidimensional relativistic electron phase and field unidimensional complex amplitude. The data obtained make more exact earlier presented preliminary data for dynamical and topological invariants of the relativistic backward-wave tube dynamics in chaotic regimes and allow to describe a scenario of transition to chaos in temporal dynamics.

DYNAMICAL AND TOPOLOGICAL INVARIANTS OF NONLINEAR DYNAMICS OF THE CHAOTIC LASER DIODES WITH AN ADDITIONAL OPTICAL INJECTION

Nonlinear chaotic dynamics of the of the chaotic laser diodes with an additional optical injection is computed within rate equations model, based on the a set of rate equations for the slave laser electric complex amplitude and carrier density. To calculate the system dynamics in a chaotic regime the known chaos theory and non-linear analysis methods such as a correlation integral algorithm, the Lyapunov’s exponents and Kolmogorov entropy analysis are used. There are listed the data of computing dynamical and topological invariants such as the correlation, embedding and Kaplan-Yorke dimensions, Lyapunov’s exponents, Kolmogorov entropy etc. New data on topological and dynamical invariants are computed and firstly presented.

The Methodology of Distinguish Between Random and Chaotic Machine Tool Oscillations

Machine tool oscillations are irregular or aperiodic. Most often, these oscillations are chaotic but, in some cases, they can be quasi-periodic or random. The methodology for characterizing oscillations in the first of two steps uses the nonparametric hypothesis tests which the observed oscillations confirmed as irregular. The methodology for the final characterization of oscillations is based on chaos quantifiers. A time series defined as the measured values of oscillations in the time domain is the basis for calculating the quantifiers of chaos. There are four quantifiers of chaos: the Lyapunov exponent, Kolmogorov entropy, fractal dimension and correlation dimension. The correlation dimension and Kolmogorov entropy are important for distinguishing between random and chaotic oscillations. Other quantifiers of chaos are not used for this purpose. The methodology requires a multidisciplinary approach based on combining Nonlinear Dynamics and Probability Theory and Statistics. The methodology can be applied to many oscillating phenomena. Therefore, the paper mainly used the term oscillations, not vibrations, chatter, etc.

Constructing Keyed Strong S-Box Using an Enhanced Quadratic Map

As the only nonlinear component for symmetric cryptography, S-Box plays an important role. An S-Box may be vulnerable because of the existence of fixed point, reverse fixed point or short iteration cycles. To construct a keyed strong S-Box, first, a 2D enhanced quadratic map (EQM) was constructed, and its dynamic behaviors were analyzed through phase diagram, Lyapunov exponent, Kolmogorov entropy, bifurcation diagram and randomness testing. The results demonstrated that the state points of EQM have uniform distribution, ergodicity and better randomness. Then a keyed strong S-Box construction algorithm was designed based on EQM, and the fixed point, reverse fixed point, and short cycles were eliminated. Experimental results verified the algorithm’s feasibility and effectiveness.

Identification of drivers’ driving habits and shift schedule correction for vehicles with automatic transmission

Resource conservation has become a hot topic, and driving habits also have a significant impact on a car’s fuel consumption. In view of the different needs of drivers with different driving habits for automatic transmission and shift characteristics, a vehicle automatic transmission, and shift correction control strategy based on driving habit recognition is proposed. Based on the analysis of drivers’ driving behavior, the phase space reconstruction method is first used to reconstruct the time series of driving control signals, and the driving habit identification and gear shift correction control are conducted based on the correlation dimension and Kolmogorov entropy evaluation index. Simulation and real car test show that the identification method based on phase space reconstruction method and driving habits evaluation index can accurately identify drivers’ driving habits. The gear shift correction control strategy based on driving habit recognition fully meets the different requirements of different drivers for the gearshift performance of vehicles and improves the intelligence degree of automatic transmission of vehicles.

Entropy as an integral operator

In this paper, we introduce the concept of entropy kernel operator for compact dynamical systems of finite Kolmogorov entropy. It is a compact positive operator on a Hilbert space. Then we state the Kolmogorov entropy in terms of the eigenvalues of the entropy kernel operator.

Denoising and Chaotic Feature Extraction of Electrocardial Signals for Driver Fatigue Detection by Kolmogorov Entropy

This paper proposes a detection method of driver fatigue by use of electrocardial signals. First, lifting wavelet transform (LWT) was used to reduce signal noise and its effect was confirmed by applying it to the denoising of a white-noise-mixed Lorenz signal. Second, phase space reconstruction was conducted for extracting chaotic features of the measured electrocardial signals. The phase diagrams show fractal geometry features even under a strong noise background. Finally, Kolmogorov entropy, which is a factor reflecting the uncertainty in and the chaotic level of a nonlinear dynamic system, was used as an indicator of driver fatigue. The effectiveness of Kolmogorov entropy in the judgment of driver fatigue was confirmed by comparison with a semantic differential (SD) subjective evaluation experiment. It was demonstrated that Kolmogorov entropy has a strong relationship with driver fatigue. It decreases when fatigue occurs. Furthermore, the influences of delay time and sampling points on Kolmogorov entropy were investigated, since the two factors are important to the actual use of the proposed detection method. Delay time may have significant influence on fatigue determination, but sampling points are relatively inconsequential. This result indicates that real-time detection can be realized by selecting a reasonably small number of sampling points.