scholarly journals Integrated Regional Enstrophy and Block Intensity as a Measure of Kolmogorov Entropy

Atmosphere ◽  
2017 ◽  
Vol 8 (12) ◽  
pp. 237 ◽  
Author(s):  
Andrew Jensen ◽  
Anthony Lupo ◽  
Igor Mokhov ◽  
Mirseid Akperov ◽  
DeVondria Reynolds
Keyword(s):  
Kolmogorov Entropy

Relevance of Correlation Dimension and Kolmogorov Entropy in the State Discriminant of Gearbox

2014 ◽  
Vol 644-650 ◽  
pp. 858-862
Author(s):  
Xiang Dong Mao ◽  
Hui Qun Yuan ◽  
Hua Gang Sun
Keyword(s):  
Correlation Dimension ◽  
Kolmogorov Entropy ◽  
Calculation Methods ◽  
Characteristic Parameters ◽  
State Monitoring ◽  
Basic Principles ◽  
Parameters Selection ◽  
Good Consistency ◽  
Chaotic Characteristic ◽  
Working Status

This paper introduces the basic principles and calculation methods for the correlation dimension and Kolmogorov entropy. By calculating the correlation dimension and Kolmogorov entropy when the gear is under different working conditions, we can analyze the inherent relationship between the two in depicting of the running condition of the gearbox. The result shows that,the correlation dimension and Kolmogorov entropy have a good consistency in the description of working status of gearbox. This conclusion not only provides a good basis for the gearbox running condition judgment and fault diagnosing, but can also provide the experimental basis for the chaotic characteristic parameters selection in state monitoring and fault diagnosing.

Development of mixing and isotropy in inviscid homogeneous turbulence

1982 ◽  
Vol 120 ◽  
pp. 155-183 ◽  
Author(s):  
Jon Lee
Keyword(s):  
Dynamical Systems ◽  
Lower Order ◽  
Stokes System ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Fourier Space ◽  
Kolmogorov Entropy ◽  
Navier Stokes Equations ◽  
Constant Energy

We have investigated a sequence of dynamical systems corresponding to spherical truncations of the incompressible three-dimensional Navier-Stokes equations in Fourier space. For lower-order truncated systems up to the spherical truncation of wavenumber radius 4, it is concluded that the inviscid Navier-Stokes system will develop mixing (and a fortiori ergodicity) on the constant energy-helicity surface, and also isotropy of the covariance spectral tensor. This conclusion is, however, drawn not directly from the mixing definition but from the observation that one cannot evolve the trajectory numerically much beyond several characteristic corre- lation times of the smallest eddy owing to the accumulation of round-off errors. The limited evolution time is a manifestation of trajectory instability (exponential orbit separation) which underlies not only mixing, but also the stronger dynamical charac- terization of positive Kolmogorov entropy (K-system).

Constructing Keyed Strong S-Box Using an Enhanced Quadratic Map

2021 ◽  
Vol 31 (10) ◽  
pp. 2150146
Author(s):  
Yuanyuan Si ◽  
Hongjun Liu ◽  
Yuehui Chen
Keyword(s):  
Phase Diagram ◽  
Fixed Point ◽  
Lyapunov Exponent ◽  
Uniform Distribution ◽  
Bifurcation Diagram ◽  
Experimental Results ◽  
Kolmogorov Entropy ◽  
Symmetric Cryptography ◽  
Quadratic Map ◽  
Nonlinear Component

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.

Simple Chaotic Electronic Circuits

2011 ◽  
pp. 68-90
Author(s):  
M.P. Hanias ◽  
G. S. Tombras
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Critical State ◽  
Strange Attractors ◽  
Embedding Dimension ◽  
Kolmogorov Entropy ◽  
Electronic Circuits ◽  
Series Analysis ◽  
Chaotic Circuits

Simple chaotic electronics circuits as diode resonator circuits, Resistor-Inductor-LED optoelectronic chaotic circuits, and Single Transistor chaotic circuits can be used as transmitters and receivers for chaotic cryptosystems. In these circuits we can change and investigate the influence of various circuit parameters to the complexity of the so generated strange attractors. Time series analysis is performed following Grassberger and Procaccia’s method while invariant parameters as correlation, and minimum embedding dimension are respectively calculated. The Kolmogorov entropy is also calculated and the RLT circuits in a critical state are examined.

scholarly journals On the Measure-Preserving Mappings with Three-Dimensions

1993 ◽  
Vol 132 ◽  
pp. 73-89
Author(s):  
Yi-Sui Sun
Keyword(s):  
Fixed Point ◽  
Invariant Manifolds ◽  
Three Dimensional ◽  
Invariant Curve ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Kolmogorov Entropy ◽  
Numerical Exploration ◽  
Area Preserving ◽  
Dimensional Mapping

AbstractWe have systematically made the numerical exploration about the perturbation extension of area-preserving mappings to three-dimensional ones, in which the fixed points of area preserving are elliptic, parabolic or hyperbolic respectively. It has been observed that: (i) the invariant manifolds in the vicinity of the fixed point generally don’t exist (ii) when the invariant curve of original two-dimensional mapping exists the invariant tubes do also in the neighbourhood of the invariant curve (iii) for the perturbation extension of area-preserving mapping the invariant manifolds can only be generated in the subset of the invariant manifolds of original two-dimensional mapping, (iv) for the perturbation extension of area preserving mappings with hyperbolic or parabolic fixed point the ordered region near and far from the invariant curve will be destroyed by perturbation more easily than the other one, This is a result different from the case with the elliptic fixed point. In the latter the ordered region near invariant curve is solid. Some of the results have been demonstrated exactly.Finally we have discussed the Kolmogorov Entropy of the mappings and studied some applications.

scholarly journals Kolmogorov entropy in the context of computability theory

2002 ◽  
Vol 271 (1-2) ◽  
pp. 15-35 ◽  
Author(s):  
Andrej A. Muchnik ◽  
Semen Ye. Positselsky
Keyword(s):  
Computability Theory ◽  
Kolmogorov Entropy
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