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Synchronization of Butterfly Fractional Order Chaotic System

Author

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  • Michal Fečkan

    (Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava, Mlynská dolina, 842 48 Bratislava, Slovakia
    Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73 Bratislava, Slovakia)

  • T. Sathiyaraj

    (Department of Mathematics, Guizhou University, Guiyang 550025, Guizhou, China)

  • JinRong Wang

    (Department of Mathematics, Guizhou University, Guiyang 550025, Guizhou, China
    School of Mathematical Sciences, Qufu Normal University, Qufu 273165, Shandong, China)

Abstract

In this paper, we study the synchronization of a nonlinear fractional system, and analyze its time response and chaotic behaviors. We represent a solution for considered system by employing the Mittag-Leffler matrix function and Jacobian matrix. Thereafter, we prove synchronization of error system between drive-response systems using stability theory and linear feedback control methods. Finally, numerical simulations are presented to show the effectiveness of the theoretical results.

Suggested Citation

  • Michal Fečkan & T. Sathiyaraj & JinRong Wang, 2020. "Synchronization of Butterfly Fractional Order Chaotic System," Mathematics, MDPI, vol. 8(3), pages 1-12, March.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:3:p:446-:d:334553
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    References listed on IDEAS

    as
    1. Laskin, Nick, 2000. "Fractional market dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 482-492.
    2. Chunlai Li & Jing Zhang, 2016. "Synchronisation of a fractional-order chaotic system using finite-time input-to-state stability," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(10), pages 2440-2448, July.
    3. Ping Zhou & Xiao-You Yang, 2011. "A Novel Hybrid Function Projective Synchronization between Different Fractional-Order Chaotic Systems," Discrete Dynamics in Nature and Society, Hindawi, vol. 2011, pages 1-15, August.
    4. Agrawal, S.K. & Srivastava, M. & Das, S., 2012. "Synchronization of fractional order chaotic systems using active control method," Chaos, Solitons & Fractals, Elsevier, vol. 45(6), pages 737-752.
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    Cited by:

    1. Ivana Eliašová & Michal Fečkan, 2022. "Poincaré Map for Discontinuous Fractional Differential Equations," Mathematics, MDPI, vol. 10(23), pages 1-16, November.

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