Observer form of the hyperbolic type generalized Lorenz system and its use for chaos synchronization

Sergej Čelikovský

Kybernetika (2004)

  • Volume: 40, Issue: 6, page [649]-664
  • ISSN: 0023-5954

Abstract

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This paper shows that a large class of chaotic systems, introduced in [S. Čelikovský and G. Chen: Hyperbolic-type generalized Lorenz system and its canonical form. In: Proc. 15th Triennial World Congress of IFAC, Barcelona 2002, CD ROM], as the hyperbolic-type generalized Lorenz system, can be systematically used to generate synchronized chaotic oscillations. While the generalized Lorenz system unifies the famous Lorenz system and Chen’s system [G. Chen and T. Ueta: Yet another chaotic attractor. Internat. J. Bifur. Chaos 9 (1999)], the hyperbolic-type generalized Lorenz system is in some way complementary to it. Synchronization of two such systems is made through a scalar coupling signal based on nonlinear observer design using special change of coordinates to the so-called observer canonical form of the hyperbolic-type generalized Lorenz system. The properties of the suggested synchronization that make it attractive for the the secure encrypted communication application are discussed in detail. Theoretical results are supported by the computer simulations, showing viability of the suggested approach.

How to cite

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Čelikovský, Sergej. "Observer form of the hyperbolic type generalized Lorenz system and its use for chaos synchronization." Kybernetika 40.6 (2004): [649]-664. <http://eudml.org/doc/33726>.

@article{Čelikovský2004,
abstract = {This paper shows that a large class of chaotic systems, introduced in [S. Čelikovský and G. Chen: Hyperbolic-type generalized Lorenz system and its canonical form. In: Proc. 15th Triennial World Congress of IFAC, Barcelona 2002, CD ROM], as the hyperbolic-type generalized Lorenz system, can be systematically used to generate synchronized chaotic oscillations. While the generalized Lorenz system unifies the famous Lorenz system and Chen’s system [G. Chen and T. Ueta: Yet another chaotic attractor. Internat. J. Bifur. Chaos 9 (1999)], the hyperbolic-type generalized Lorenz system is in some way complementary to it. Synchronization of two such systems is made through a scalar coupling signal based on nonlinear observer design using special change of coordinates to the so-called observer canonical form of the hyperbolic-type generalized Lorenz system. The properties of the suggested synchronization that make it attractive for the the secure encrypted communication application are discussed in detail. Theoretical results are supported by the computer simulations, showing viability of the suggested approach.},
author = {Čelikovský, Sergej},
journal = {Kybernetika},
keywords = {nonlinear; chaotic; synchronization; observer; nonlinear system; chaotic system; synchronization; observer},
language = {eng},
number = {6},
pages = {[649]-664},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Observer form of the hyperbolic type generalized Lorenz system and its use for chaos synchronization},
url = {http://eudml.org/doc/33726},
volume = {40},
year = {2004},
}

TY - JOUR
AU - Čelikovský, Sergej
TI - Observer form of the hyperbolic type generalized Lorenz system and its use for chaos synchronization
JO - Kybernetika
PY - 2004
PB - Institute of Information Theory and Automation AS CR
VL - 40
IS - 6
SP - [649]
EP - 664
AB - This paper shows that a large class of chaotic systems, introduced in [S. Čelikovský and G. Chen: Hyperbolic-type generalized Lorenz system and its canonical form. In: Proc. 15th Triennial World Congress of IFAC, Barcelona 2002, CD ROM], as the hyperbolic-type generalized Lorenz system, can be systematically used to generate synchronized chaotic oscillations. While the generalized Lorenz system unifies the famous Lorenz system and Chen’s system [G. Chen and T. Ueta: Yet another chaotic attractor. Internat. J. Bifur. Chaos 9 (1999)], the hyperbolic-type generalized Lorenz system is in some way complementary to it. Synchronization of two such systems is made through a scalar coupling signal based on nonlinear observer design using special change of coordinates to the so-called observer canonical form of the hyperbolic-type generalized Lorenz system. The properties of the suggested synchronization that make it attractive for the the secure encrypted communication application are discussed in detail. Theoretical results are supported by the computer simulations, showing viability of the suggested approach.
LA - eng
KW - nonlinear; chaotic; synchronization; observer; nonlinear system; chaotic system; synchronization; observer
UR - http://eudml.org/doc/33726
ER -

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