中国物理B ›› 2014, Vol. 23 ›› Issue (6): 60501-060501.doi: 10.1088/1674-1056/23/6/060501

• GENERAL • 上一篇    下一篇

Synchronization of the fractional-order generalized augmented Lü system and its circuit implementation

薛薇a, 徐进康a, 仓诗建b, 贾红艳a   

  1. 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
  • 收稿日期:2013-09-09 修回日期:2013-12-16 出版日期:2014-06-15 发布日期:2014-06-15
  • 基金资助:
    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).

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   

  1. 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
  • Received:2013-09-09 Revised:2013-12-16 Online:2014-06-15 Published:2014-06-15
  • Contact: Xue Wei E-mail:xuewei@tust.edu.cn
  • Supported by:
    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).

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摘要： 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.

关键词: fractional-order generalized augmented Lü, system, nonlinear feedback synchronization, numerical simulation, circuit design

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.

Key words: fractional-order generalized augmented Lü, system, nonlinear feedback synchronization, numerical simulation, circuit design

中图分类号:  (Nonlinear dynamics and chaos)

  • 05.45.-a
05.45.Pq (Numerical simulations of chaotic systems)