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A New Fractional-Order Jerk System and Its Hybrid Synchronization

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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, a new Jerk chaotic system with a piecewise nonlinear (PWNL) function and its fractional-order (FO) generalization are proposed. Both the FO and the PWNL function, serving as chaotic generators, make the proposed system more adopting for electrical engineering applications. The highly complex dynamics of the novel system are investigated by theoretical analysis pointing out its elementary characteristics such as the Lyapunov exponents, the attractor forms and the equilibrium points. To focus on the application values of the novel FO system in multilateral communication, hybrid synchronization (HS) with ring connection is investigated. For such schema, where all systems are coupled on a chain, complete synchronization (CS) and complete anti-synchronization (AS) co-exist where the state variables of the first system couple the Nth system and the state variables of the Nth system couple the \((N-1)th\) system. Simulations results prove that the synchronization problem is achieved with success for the multiple coupled FO systems.

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Authors and Affiliations

  1. National Institute of Applied Sciences and Technology, Centre Urbain Nord BP.676, 1080, Tunis Cedex, Tunisia

    Abir Lassoued & Olfa Boubaker

Authors
  1. Abir Lassoued
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  2. Olfa Boubaker
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Corresponding author

Correspondence to Abir Lassoued .

Editor information

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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Lassoued, A., Boubaker, O. (2017). A New Fractional-Order Jerk System and Its Hybrid Synchronization . 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_24

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  • DOI: https://doi.org/10.1007/978-3-319-50249-6_24

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-50248-9

  • Online ISBN: 978-3-319-50249-6

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