Nonlinear Dynamics

, Volume 55, Issue 1–2, pp 43–53

Chaos synchronization of two different chaotic complex Chen and Lü systems

  • Gamal M. Mahmoud
  • Tassos Bountis
  • G. M. AbdEl-Latif
  • Emad E. Mahmoud
Original Paper

DOI: 10.1007/s11071-008-9343-5

Cite this article as:
Mahmoud, G.M., Bountis, T., AbdEl-Latif, G.M. et al. Nonlinear Dyn (2009) 55: 43. doi:10.1007/s11071-008-9343-5

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.

Keywords

Chaos Synchronization Active control Error system Complex 

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  • Gamal M. Mahmoud
    • 1
  • Tassos Bountis
    • 2
  • G. M. AbdEl-Latif
    • 3
  • Emad E. Mahmoud
    • 3
  1. 1.Department of Mathematics, Faculty of ScienceAssiut UniversityAssiutEgypt
  2. 2.Department of Mathematics and Center for Research and Applications for Nonlinear SystemsUniversity of PatrasPatrasGreece
  3. 3.Department of Mathematics, Faculty of ScienceSohag UniversitySohagEgypt

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