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Fractional Inverse Generalized Chaos Synchronization Between Different Dimensional Systems

  • Adel Ouannas
  • Ahmad Taher Azar
  • Toufik Ziar
  • Sundarapandian Vaidyanathan
Chapter
Part of the Studies in Computational Intelligence book series (SCI, volume 688)

Abstract

In this chapter, new control schemes to achieve inverse generalizedsynchronization (IGS) between fractional order chaotic (hyperchaotic) systems with different dimensions are presented. Specifically, given a fractional master system with dimension n and a fractional slave system with dimension m, the proposed approach enables each master system state to be synchronized with a functional relationship of slave system states. The method, based on the fractional Lyapunov approach and stability property of integer-order linear differential systems, presents some useful features: (i) it enables synchronization to be achieved for both cases \(n<m\) and \(n>m\); (ii) it is rigorous, being based on theorems; (iii) it can be readily applied to any chaotic (hyperchaotic) fractional systems. Finally, the capability of the approach is illustrated by synchronization examples.

Keywords

Chaos Inverse generalized synchronization Fractional systems Different dimensions Fractional lyapunov approach 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Adel Ouannas
    • 1
  • Ahmad Taher Azar
    • 2
    • 3
  • Toufik Ziar
    • 4
  • Sundarapandian Vaidyanathan
    • 5
  1. 1.Laboratory of Mathematics, Informatics and Systems (LAMIS)University of Larbi TebessiTebessaAlgeria
  2. 2.Faculty of Computers and InformationBenha UniversityBenhaEgypt
  3. 3.Nanoelectronics Integrated Systems Center (NISC), Nile UniversityCairoEgypt
  4. 4.Department of Material SciencesUniversity of TebessaTebessaAlgeria
  5. 5.Research and Development Centre, Vel Tech University, AvadiChennaiIndia

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