Generalized Synchronization of Fractional Order Chaotic Systems with Time-Delay

Sha Wang; Jie Li; Renhao Jin

doi:doi:10.11648/j.ijmea.20160406.14

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Generalized Synchronization of Fractional Order Chaotic Systems with Time-Delay

Sha Wang, Jie Li, Renhao Jin

Published in International Journal of Mechanical Engineering and Applications (Volume 4, Issue 6)

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.

Published in	International Journal of Mechanical Engineering and Applications (Volume 4, Issue 6)
DOI	10.11648/j.ijmea.20160406.14
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), 2016. Published by Science Publishing Group

Keywords

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

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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://article.sciencepublishinggroup.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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Author Information

Sha Wang

School of Information, Beijing Wuzi University, Beijing, China
Jie Li

School of Information, Beijing Wuzi University, Beijing, China
Renhao Jin

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

Copy | Download

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

Copy | Download

@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://article.sciencepublishinggroup.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}
}

Copy | Download

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  -

Copy | Download