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Fractional Inverse Generalized Chaos Synchronization Between Different Dimensional Systems

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Fractional Order Control and Synchronization of Chaotic Systems

Part of the book series: Studies in Computational Intelligence ((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.

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Authors and Affiliations

  1. Laboratory of Mathematics, Informatics and Systems (LAMIS), University of Larbi Tebessi, 12002, Tebessa, Algeria

    Adel Ouannas

  2. Faculty of Computers and Information, Benha University, Benha, Egypt

    Ahmad Taher Azar

  3. Nanoelectronics Integrated Systems Center (NISC), Nile University, Cairo, Egypt

    Ahmad Taher Azar

  4. Department of Material Sciences, University of Tebessa, 12002, Tebessa, Algeria

    Toufik Ziar

  5. Research and Development Centre, Vel Tech University, Avadi, Chennai, 600062, Tamil Nadu, India

    Sundarapandian Vaidyanathan

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  1. Adel Ouannas
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  4. Sundarapandian Vaidyanathan
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Correspondence to Ahmad Taher Azar .

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  1. Faculty of Computers and Information, Benha University Faculty of Computers and Information, AND Nanoelectronics Integrated Systems Center (NISC), Nile University, Egypt. , Benha, Egypt

    Ahmad Taher Azar

  2. Research and Development Centre, Vel Tech University Research and Development Centre, Chennai, Tamil Nadu, India

    Sundarapandian Vaidyanathan

  3. Department of Mathematics and CS, University of Tebessa Department of Mathematics and CS, Tebessa, Algeria

    Adel Ouannas

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Ouannas, A., Azar, A.T., Ziar, T., Vaidyanathan, S. (2017). Fractional Inverse Generalized Chaos Synchronization Between Different Dimensional Systems. In: Azar, A., Vaidyanathan, S., Ouannas, A. (eds) Fractional Order Control and Synchronization of Chaotic Systems. Studies in Computational Intelligence, vol 688. Springer, Cham. https://doi.org/10.1007/978-3-319-50249-6_18

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