International Journal of Mechanical Engineering and Applications

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Generalized Synchronization of Fractional Order Chaotic Systems with Time-Delay

Received: 22 July 2016    Accepted: 27 October 2016    Published: 17 December 2016
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Abstract

Generalized synchronization of time-delayed fractional order chaotic systems is investigated. According to the stability theorem of linear fractional differential systems with multiple time-delays, a nonlinear fractional order controller is designed for the synchronization of systems with identical and non-identical derivative orders. Both complete synchronization and projective synchronization also can be realized based on the proposed controller. The effectiveness and robustness of the controller are verified in the numerical simulations.

DOI 10.11648/j.ijmea.20160406.14
Published in International Journal of Mechanical Engineering and Applications (Volume 4, Issue 6, December 2016)
Page(s) 232-241
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Fractional Order, Chaos, Nonlinear Control, Generalized Synchronization, Time-Delay

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Author Information
  • School of Information, Beijing Wuzi University, Beijing, China

  • School of Information, Beijing Wuzi University, Beijing, China

  • School of Information, Beijing Wuzi University, Beijing, China

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  • APA Style

    Sha Wang, Jie Li, Renhao Jin. (2016). Generalized Synchronization of Fractional Order Chaotic Systems with Time-Delay. International Journal of Mechanical Engineering and Applications, 4(6), 232-241. https://doi.org/10.11648/j.ijmea.20160406.14

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    ACS Style

    Sha Wang; Jie Li; Renhao Jin. Generalized Synchronization of Fractional Order Chaotic Systems with Time-Delay. Int. J. Mech. Eng. Appl. 2016, 4(6), 232-241. doi: 10.11648/j.ijmea.20160406.14

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    AMA Style

    Sha Wang, Jie Li, Renhao Jin. Generalized Synchronization of Fractional Order Chaotic Systems with Time-Delay. Int J Mech Eng Appl. 2016;4(6):232-241. doi: 10.11648/j.ijmea.20160406.14

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  • @article{10.11648/j.ijmea.20160406.14,
      author = {Sha Wang and Jie Li and Renhao Jin},
      title = {Generalized Synchronization of Fractional Order Chaotic Systems with Time-Delay},
      journal = {International Journal of Mechanical Engineering and Applications},
      volume = {4},
      number = {6},
      pages = {232-241},
      doi = {10.11648/j.ijmea.20160406.14},
      url = {https://doi.org/10.11648/j.ijmea.20160406.14},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ijmea.20160406.14},
      abstract = {Generalized synchronization of time-delayed fractional order chaotic systems is investigated. According to the stability theorem of linear fractional differential systems with multiple time-delays, a nonlinear fractional order controller is designed for the synchronization of systems with identical and non-identical derivative orders. Both complete synchronization and projective synchronization also can be realized based on the proposed controller. The effectiveness and robustness of the controller are verified in the numerical simulations.},
     year = {2016}
    }
    

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  • TY  - JOUR
    T1  - Generalized Synchronization of Fractional Order Chaotic Systems with Time-Delay
    AU  - Sha Wang
    AU  - Jie Li
    AU  - Renhao Jin
    Y1  - 2016/12/17
    PY  - 2016
    N1  - https://doi.org/10.11648/j.ijmea.20160406.14
    DO  - 10.11648/j.ijmea.20160406.14
    T2  - International Journal of Mechanical Engineering and Applications
    JF  - International Journal of Mechanical Engineering and Applications
    JO  - International Journal of Mechanical Engineering and Applications
    SP  - 232
    EP  - 241
    PB  - Science Publishing Group
    SN  - 2330-0248
    UR  - https://doi.org/10.11648/j.ijmea.20160406.14
    AB  - Generalized synchronization of time-delayed fractional order chaotic systems is investigated. According to the stability theorem of linear fractional differential systems with multiple time-delays, a nonlinear fractional order controller is designed for the synchronization of systems with identical and non-identical derivative orders. Both complete synchronization and projective synchronization also can be realized based on the proposed controller. The effectiveness and robustness of the controller are verified in the numerical simulations.
    VL  - 4
    IS  - 6
    ER  - 

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