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Nonlinear Dynamics

, Volume 83, Issue 4, pp 1885–1893 | Cite as

Generalization of combination–combination synchronization of chaotic n-dimensional fractional-order dynamical systems

  • Gamal M. MahmoudEmail author
  • Tarek M. Abed-Elhameed
  • Mansour E. Ahmed
Original Paper

Abstract

The generalization of combination–combination (C–C) synchronization of chaotic n-dimensional (nD) fractional-order \((0<\alpha \le 1)\) dynamical systems is studied. Firstly, we replace arbitrary four chaotic nD ordinary dynamical systems by four chaotic nD fractional-order dynamical systems which have unique solutions. Secondly, we extend the scheme of a recent paper (Sun et al. in Nonlinear Dyn 73: 1211–1222, 2013) to study the generalization of C–C synchronization among four nD fractional-order dynamical systems. Examples of combination–combination synchronization among four identical or different of 6D chaotic fractional-order systems are discussed. The analytical formula of the control functions is tested numerically to achieve C–C synchronization, and good agreement is found.

Keywords

Combination–combination synchronization Chaotic dynamical system Fractional-order dynamical system 

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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Gamal M. Mahmoud
    • 1
    Email author
  • Tarek M. Abed-Elhameed
    • 1
  • Mansour E. Ahmed
    • 1
    • 2
  1. 1.Department of Mathematics, Faculty of ScienceAssiut UniversityAssiutEgypt
  2. 2.Department of Mathematics, Faculty of University College in AljamoumUmm Al-Qura UniversityMakkahKingdom of Saudi Arabia

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