Dynamics Models of Synchronized Piecewise Linear Discrete Chaotic Systems of High Order

This paper deals with the methods for investigating the nonlinear dynamics of discrete chaotic systems (DCS) applied to piecewise linear systems of the third order. The paper proposes an approach to the analysis of the systems under research and their improvement. Thus, effective and mathematically...

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Bibliographic Details
Published in:Symmetry (Basel) 2019-02, Vol.11 (2), p.236
Main Authors: Sokolov, Sergei, Zhilenkov, Anton, Chernyi, Sergei, Nyrkov, Anatoliy, Mamunts, David
Format: Article
Language:English
Subjects:
algorithm
Algorithms
Chaos theory
chaotic system
Data processing
Discrete systems
Dynamic characteristics
Dynamical systems
Eigenvalues
linear discrete
Linear systems
Motion stability
nonlinear
Nonlinear dynamics
Numerical analysis
Synchronism
synchronized
System effectiveness
Systems analysis
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Summary:This paper deals with the methods for investigating the nonlinear dynamics of discrete chaotic systems (DCS) applied to piecewise linear systems of the third order. The paper proposes an approach to the analysis of the systems under research and their improvement. Thus, effective and mathematically sound methods for the analysis of nonlinear motions in the models under consideration are proposed. It makes it possible to obtain simple calculated relations for determining the basic dynamic characteristics of systems. Based on these methods, the authors developed algorithms for calculating the dynamic characteristics of discrete systems, i.e. areas of the existence of steady-state motion, areas of stability, capture band, and parameters of transients. By virtue of the developed methods and algorithms, the dynamic modes of several models of discrete phase synchronization systems can be analyzed. They are as follows: Pulsed and digital different orders, dual-ring systems of various types, including combined ones, and systems with cyclic interruption of auto-tuning. The efficiency of various devices for information processing, generation and stabilization could be increased by using the mentioned discrete synchronization systems on the grounds of the results of the analysis. We are now developing original software for analyzing the dynamic characteristics of various classes of discrete phase synchronization systems, based on the developed methods and algorithms.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym11020236