Chaos synchronization of two different chaotic complex Chen and Lü systems

Gamal M. Mahmoud, Tassos Bountis, G. M. Abdel-Latif, Emad E. Mahmoud

Research output: Contribution to journalArticle

61 Citations (Scopus)

Abstract

This paper investigates the phenomenon of chaos synchronization of two different chaotic complex systems of the Chen and Lü type via the methods of active control and global synchronization. In this regard, it generalizes earlier work on the synchronization of two identical oscillators in cases where the drive and response systems are different, the parameter space is larger, and the dimensionality increases due to the complexification of the dependent variables. The idea of chaos synchronization is to use the output of the drive system to control the response system so that the output of the response system converges to the output of the drive system as time increases. Lyapunov functions are derived to prove that the differences in the dynamics of the two systems converge to zero exponentially fast, explicit expressions are given for the control functions and numerical simulations are presented to illustrate the success of our chaos synchronization techniques. We also point out that the global synchronization method is better suited for synchronizing identical chaotic oscillators, as it has serious limitations when applied to the case where the drive and response systems are different.

Original languageEnglish
Pages (from-to)43-53
Number of pages11
JournalNonlinear Dynamics
Volume55
Issue number1-2
DOIs
Publication statusPublished - Jan 2009
Externally publishedYes

Fingerprint

Chen System
L-system
Chaos Synchronization
Chaos theory
Complex Systems
Synchronization
Global Synchronization
Output
Converge
Chaotic Oscillator
Complexification
Lyapunov functions
Active Control
Control Function
Large scale systems
Lyapunov Function
Chaotic System
Dimensionality
Parameter Space
Computer simulation

Keywords

  • Active control
  • Chaos
  • Complex
  • Error system
  • Synchronization

ASJC Scopus subject areas

  • Applied Mathematics
  • Mechanical Engineering
  • Aerospace Engineering
  • Ocean Engineering
  • Electrical and Electronic Engineering
  • Control and Systems Engineering

Cite this

Mahmoud, G. M., Bountis, T., Abdel-Latif, G. M., & Mahmoud, E. E. (2009). Chaos synchronization of two different chaotic complex Chen and Lü systems. Nonlinear Dynamics, 55(1-2), 43-53. https://doi.org/10.1007/s11071-008-9343-5

Chaos synchronization of two different chaotic complex Chen and Lü systems. / Mahmoud, Gamal M.; Bountis, Tassos; Abdel-Latif, G. M.; Mahmoud, Emad E.

In: Nonlinear Dynamics, Vol. 55, No. 1-2, 01.2009, p. 43-53.

Research output: Contribution to journalArticle

Mahmoud, GM, Bountis, T, Abdel-Latif, GM & Mahmoud, EE 2009, 'Chaos synchronization of two different chaotic complex Chen and Lü systems', Nonlinear Dynamics, vol. 55, no. 1-2, pp. 43-53. https://doi.org/10.1007/s11071-008-9343-5
Mahmoud, Gamal M. ; Bountis, Tassos ; Abdel-Latif, G. M. ; Mahmoud, Emad E. / Chaos synchronization of two different chaotic complex Chen and Lü systems. In: Nonlinear Dynamics. 2009 ; Vol. 55, No. 1-2. pp. 43-53.
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