A new approach to generalized chaos synchronization based on the stability of the error system

Zhi Liang Zhu; Shuping Li; Hai Yu

Kybernetika (2008)

  • Volume: 44, Issue: 4, page 492-500
  • ISSN: 0023-5954

Abstract

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With a chaotic system being divided into linear and nonlinear parts, a new approach is presented to realize generalized chaos synchronization by using feedback control and parameter commutation. Based on a linear transformation, the problem of generalized synchronization (GS) is transformed into the stability problem of the synchronous error system, and an existence condition for GS is derived. Furthermore, the performance of GS can be improved according to the configuration of the GS velocity. Further generalization and appropriation can be acquired without a stability requirement for the chaotic system’s linear part. The Lorenz system and a hyperchaotic system are taken for illustration and verification and the results of the simulation indicate that the method is effective.

How to cite

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Zhu, Zhi Liang, Li, Shuping, and Yu, Hai. "A new approach to generalized chaos synchronization based on the stability of the error system." Kybernetika 44.4 (2008): 492-500. <http://eudml.org/doc/33944>.

@article{Zhu2008,
abstract = {With a chaotic system being divided into linear and nonlinear parts, a new approach is presented to realize generalized chaos synchronization by using feedback control and parameter commutation. Based on a linear transformation, the problem of generalized synchronization (GS) is transformed into the stability problem of the synchronous error system, and an existence condition for GS is derived. Furthermore, the performance of GS can be improved according to the configuration of the GS velocity. Further generalization and appropriation can be acquired without a stability requirement for the chaotic system’s linear part. The Lorenz system and a hyperchaotic system are taken for illustration and verification and the results of the simulation indicate that the method is effective.},
author = {Zhu, Zhi Liang, Li, Shuping, Yu, Hai},
journal = {Kybernetika},
keywords = {chaotic system; generalized synchronization; configuration of poles; synchronous velocity; chaotic system; generalized synchronization; configuration of poles; synchronous velocity},
language = {eng},
number = {4},
pages = {492-500},
publisher = {Institute of Information Theory and Automation AS CR},
title = {A new approach to generalized chaos synchronization based on the stability of the error system},
url = {http://eudml.org/doc/33944},
volume = {44},
year = {2008},
}

TY - JOUR
AU - Zhu, Zhi Liang
AU - Li, Shuping
AU - Yu, Hai
TI - A new approach to generalized chaos synchronization based on the stability of the error system
JO - Kybernetika
PY - 2008
PB - Institute of Information Theory and Automation AS CR
VL - 44
IS - 4
SP - 492
EP - 500
AB - With a chaotic system being divided into linear and nonlinear parts, a new approach is presented to realize generalized chaos synchronization by using feedback control and parameter commutation. Based on a linear transformation, the problem of generalized synchronization (GS) is transformed into the stability problem of the synchronous error system, and an existence condition for GS is derived. Furthermore, the performance of GS can be improved according to the configuration of the GS velocity. Further generalization and appropriation can be acquired without a stability requirement for the chaotic system’s linear part. The Lorenz system and a hyperchaotic system are taken for illustration and verification and the results of the simulation indicate that the method is effective.
LA - eng
KW - chaotic system; generalized synchronization; configuration of poles; synchronous velocity; chaotic system; generalized synchronization; configuration of poles; synchronous velocity
UR - http://eudml.org/doc/33944
ER -

References

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  9. Kocarev L., Parlitz U., Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems, Phys. Rev. Lett. 11 (1996), 76, 1816–1819 (1996) 
  10. Lorenz E. N., Deterministic nonperiodic flow, J. Atmospheric Sci. 20 (1963), 1. 130–141 (1963) 
  11. Pecora M., Carroll L., Synchronization in chaotic systems, Phys. Rev. Lett. 64 (1990), 8, 821–823 (1990) Zbl0938.37019MR1038263
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