IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i3p446-d334553.html
   My bibliography  Save this article

Synchronization of Butterfly Fractional Order Chaotic System

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/3/446/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/3/446/
    Download Restriction: no
    ---><---

    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. 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.
    3. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

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

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Balootaki, Mohammad Ahmadi & Rahmani, Hossein & Moeinkhah, Hossein & Mohammadzadeh, Ardashir, 2020. "On the Synchronization and Stabilization of fractional-order chaotic systems: Recent advances and future perspectives," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    2. Peng, Qiu & Jian, Jigui, 2023. "Synchronization analysis of fractional-order inertial-type neural networks with time delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 62-77.
    3. Yi Chen & Jing Dong & Hao Ni, 2021. "ɛ-Strong Simulation of Fractional Brownian Motion and Related Stochastic Differential Equations," Mathematics of Operations Research, INFORMS, vol. 46(2), pages 559-594, May.
    4. Ge, Zheng-Ming & Yi, Chang-Xian, 2007. "Chaos in a nonlinear damped Mathieu system, in a nano resonator system and in its fractional order systems," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 42-61.
    5. Pratap, A. & Raja, R. & Cao, J. & Lim, C.P. & Bagdasar, O., 2019. "Stability and pinning synchronization analysis of fractional order delayed Cohen–Grossberg neural networks with discontinuous activations," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 241-260.
    6. Tam, Lap Mou & Si Tou, Wai Meng, 2008. "Parametric study of the fractional-order Chen–Lee system," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 817-826.
    7. Wang, Fei & Yang, Yongqing & Hu, Manfeng & Xu, Xianyun, 2015. "Projective cluster synchronization of fractional-order coupled-delay complex network via adaptive pinning control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 434(C), pages 134-143.
    8. G. Fern'andez-Anaya & L. A. Quezada-T'ellez & B. Nu~nez-Zavala & D. Brun-Battistini, 2019. "Katugampola Generalized Conformal Derivative Approach to Inada Conditions and Solow-Swan Economic Growth Model," Papers 1907.00130, arXiv.org.
    9. Wafaa S. Sayed & Moheb M. R. Henein & Salwa K. Abd-El-Hafiz & Ahmed G. Radwan, 2017. "Generalized Dynamic Switched Synchronization between Combinations of Fractional-Order Chaotic Systems," Complexity, Hindawi, vol. 2017, pages 1-17, February.
    10. Wang, Fei & Zheng, Zhaowen, 2019. "Quasi-projective synchronization of fractional order chaotic systems under input saturation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    11. Lu, Jun Guo & Chen, Guanrong, 2006. "A note on the fractional-order Chen system," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 685-688.
    12. Liang, Yuqin & Jia, Yunfeng, 2022. "Stability and Hopf bifurcation of a diffusive plankton model with time-delay and mixed nonlinear functional responses," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    13. Mostaghimi, Soudeh & Nazarimehr, Fahimeh & Jafari, Sajad & Ma, Jun, 2019. "Chemical and electrical synapse-modulated dynamical properties of coupled neurons under magnetic flow," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 42-56.
    14. Sheu, Long-Jye & Chen, Hsien-Keng & Chen, Juhn-Horng & Tam, Lap-Mou & Chen, Wen-Chin & Lin, Kuang-Tai & Kang, Yuan, 2008. "Chaos in the Newton–Leipnik system with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 98-103.
    15. Kocamaz, Uğur Erkin & Cevher, Barış & Uyaroğlu, Yılmaz, 2017. "Control and synchronization of chaos with sliding mode control based on cubic reaching rule," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 92-98.
    16. Nazarimehr, Fahimeh & Panahi, Shirin & Jalili, Mahdi & Perc, Matjaž & Jafari, Sajad & Ferčec, Brigita, 2020. "Multivariable coupling and synchronization in complex networks," Applied Mathematics and Computation, Elsevier, vol. 372(C).
    17. Laskin, Nick, 2018. "Valuing options in shot noise market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 518-533.
    18. Ali Balcı, Mehmet, 2017. "Time fractional capital-induced labor migration model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 477(C), pages 91-98.
    19. Xuan-Bing Yang & Yi-Gang He & Chun-Lai Li, 2018. "Dynamics Feature and Synchronization of a Robust Fractional-Order Chaotic System," Complexity, Hindawi, vol. 2018, pages 1-12, December.
    20. Trinidad Segovia, J.E. & Fernández-Martínez, M. & Sánchez-Granero, M.A., 2012. "A note on geometric method-based procedures to calculate the Hurst exponent," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(6), pages 2209-2214.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:8:y:2020:i:3:p:446-:d:334553. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.