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Open AccessArticle

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

Department of Integrated Information Security, Admiral Makarov State University of Maritime and Inland Shipping, Saint-Petersburg 198035, Russia
Faculty of management systems and robotics, ITMO University, Saint-Petersburg 197101, Russia
Author to whom correspondence should be addressed.
Symmetry 2019, 11(2), 236;
Received: 17 January 2019 / Revised: 30 January 2019 / Accepted: 11 February 2019 / Published: 15 February 2019
(This article belongs to the Special Issue Discrete Mathematics and Symmetry)
PDF [2000 KB, uploaded 15 February 2019]


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. View Full-Text
Keywords: nonlinear; synchronized; linear discrete; chaotic system; algorithm nonlinear; synchronized; linear discrete; chaotic system; algorithm

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Sokolov, S.; Zhilenkov, A.; Chernyi, S.; Nyrkov, A.; Mamunts, D. Dynamics Models of Synchronized Piecewise Linear Discrete Chaotic Systems of High Order. Symmetry 2019, 11, 236.

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