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A Study on Coexistence of Different Types of Synchronization Between Different Dimensional Fractional Chaotic 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 study, robust approaches are proposed to investigate the problem of the coexistence of various types of synchronization between different dimensional fractional chaotic systems. Based on stability theory of linear fractional order systems, the co-existence of full state hybrid function projective synchronization (FSHFPS), inverse generalized synchronization (IGS), inverse full state hybrid projective synchronization (IFSHPS) and generalized synchronization (GS) is demonstrated. Using integer-order Lyapunov stability theory and fractional Lyapunov method, the co-existence of FSHFPS, inverse full state hybrid function projective synchronization (IFSHFPS), IGS and GS is also proved. Finally, numerical results are reported, with the aim to illustrate the capabilities of the novel schemes proposed herein.

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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, Banha, 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. Nanoelectronics Integrated Systems Center (NISC), Nile University, Giza, Egypt

    Ahmed G. Radwan

  6. Engineering Mathematics and Physics Department, Cairo University, Cairo, Egypt

    Ahmed G. Radwan

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  1. Adel Ouannas
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  2. Ahmad Taher Azar
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  3. Toufik Ziar
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  4. Ahmed G. Radwan
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Correspondence to Ahmad Taher Azar .

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Editors and Affiliations

  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., Radwan, A.G. (2017). A Study on Coexistence of Different Types of Synchronization Between Different Dimensional Fractional Chaotic 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_22

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