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Synchronization of the fractional-order generalized augmented Lü system and its circuit implementation |
| Xue Wei (薛薇)a, Xu Jin-Kang (徐进康)a, Cang Shi-Jian (仓诗建)b, Jia Hong-Yan (贾红艳)a |
a Department of Automation, Tianjin University of Science and Technology, Tianjin 300222, China;
b Department of Industry Design, Tianjin University of Science and Technology, Tianjin 300222, China |
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Abstract In this paper, the synchronization of the fractional-order generalized augmented Lü system is investigated. Based on the predictor-corrector method, we obtain phase portraits, bifurcation diagrams, Lyapunov exponent spectra, and Poincaré maps of the fractional-order system and find that a four-wing chaotic attractor exists in the system when the system parameters change within certain ranges. Further, by varying the system parameters, rich dynamical behaviors occur in the 2.7-order system. According to the stability theory of a fractional-order linear system, and adopting the linearization by feedback method, we have designed a nonlinear feedback controller in our theoretical analysis to implement the synchronization of the drive system with the response system. In addition, the synchronization is also shown by an electronic circuit implementation for the 2.7-order system. The obtained experiment results accord with the theoretical analyses, which further demonstrate the feasibility and effectiveness of the proposed synchronization scheme.
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Received: 09 September 2013
Revised: 16 December 2013
Accepted manuscript online:
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PACS:
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05.45.-a
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(Nonlinear dynamics and chaos)
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05.45.Pq
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(Numerical simulations of chaotic systems)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant No. 61174094) and the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 11202148). |
Corresponding Authors:
Xue Wei
E-mail: xuewei@tust.edu.cn
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Cite this article:
Xue Wei (薛薇), Xu Jin-Kang (徐进康), Cang Shi-Jian (仓诗建), Jia Hong-Yan (贾红艳) Synchronization of the fractional-order generalized augmented Lü system and its circuit implementation 2014 Chin. Phys. B 23 060501
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| [1] |
Li G H 2005 Chin. Phys. 14 472
|
| [2] |
Zhang R X and Yang S P 2008 Acta Phys. Sin. 57 6852 (in Chinese)
|
| [3] |
Qi D L, Wang Q and Yang J 2011 Chin. Phys. B 20 100505
|
| [4] |
Li M and Liu C X 2010 Chin. Phys. B 19 100504
|
| [5] |
Zhang R X and Yang S P 2011 Nonlinear Dyn. 66 831
|
| [6] |
Wang X Y, Zhang Y L, Lin D and Zhang N 2011 Chin. Phys. B 20 030506
|
| [7] |
Wu C J, Zhang Y B and Yang N N 2011 Chin. Phys. B 20 060505
|
| [8] |
Zhang R X and Yang S P 2011 Chin. Phys. B 20 090512
|
| [9] |
Liu L, Liang D L and Liu C X 2012 Nonlinear Dyn. 69 1929
|
| [10] |
Huang L L and Ma N 2012 Acta Phys. Sin. 61 160510 (in Chinese)
|
| [11] |
L J H, Chen G R and Cheng D Z 2004 Int. J. Bifur. Chaos 14 1507
|
| [12] |
Qiao X H and Bao B C 2009 Acta Phys. Sin. 58 8152 (in Chinese)
|
| [13] |
Matignon D 1996 in: IMACS, IEEE-SMC, Lille, France 963
|
| [14] |
Ahmad W M, and Sprott J C 2003 Chaos, Solitons & Fractals 16 339
|
| [15] |
Wang Z and Sun W 2012 Computer Engineering & Science 34 187
|
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