中国物理B ›› 2017, Vol. 26 ›› Issue (6): 60503-060503.doi: 10.1088/1674-1056/26/6/060503

• GENERAL • 上一篇    下一篇

Attempt to generalize fractional-order electric elements to complex-order ones

Gangquan Si(司刚全), Lijie Diao(刁利杰), Jianwei Zhu(朱建伟), Yuhang Lei(雷妤航), Yanbin Zhang(张彦斌)   

  1. State Key Laboratory of Electrical Insulation and Power Equipment, Xi'an Jiaotong University, Xi'an 710049, China
  • 收稿日期:2017-03-02 修回日期:2017-03-22 出版日期:2017-06-05 发布日期:2017-06-05
  • 通讯作者: Gangquan Si E-mail:sigangquan@mail.xjtu.edu.cn

Attempt to generalize fractional-order electric elements to complex-order ones

Gangquan Si(司刚全), Lijie Diao(刁利杰), Jianwei Zhu(朱建伟), Yuhang Lei(雷妤航), Yanbin Zhang(张彦斌)   

  1. State Key Laboratory of Electrical Insulation and Power Equipment, Xi'an Jiaotong University, Xi'an 710049, China
  • Received:2017-03-02 Revised:2017-03-22 Online:2017-06-05 Published:2017-06-05
  • Contact: Gangquan Si E-mail:sigangquan@mail.xjtu.edu.cn

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摘要： The complex derivative Dα±jβ, with α, β∈R+ is a generalization of the concept of integer derivative, where α=1, β=0. Fractional-order electric elements and circuits are becoming more and more attractive. In this paper, the complex-order electric elements concept is proposed for the first time, and the complex-order elements are modeled and analyzed. Some interesting phenomena are found that the real part of the order affects the phase of output signal, and the imaginary part affects the amplitude for both the complex-order capacitor and complex-order memristor. More interesting is that the complex-order capacitor can do well at the time of fitting electrochemistry impedance spectra. The complex-order memristor is also analyzed. The area inside the hysteresis loops increases with the increasing of the imaginary part of the order and decreases with the increasing of the real part. Some complex case of complex-order memristors hysteresis loops are analyzed at last, whose loop has touching points beyond the origin of the coordinate system.

关键词: complex derivative, fractional-order elements, imaginary and real part, memristor

Abstract: The complex derivative Dα±jβ, with α, β∈R+ is a generalization of the concept of integer derivative, where α=1, β=0. Fractional-order electric elements and circuits are becoming more and more attractive. In this paper, the complex-order electric elements concept is proposed for the first time, and the complex-order elements are modeled and analyzed. Some interesting phenomena are found that the real part of the order affects the phase of output signal, and the imaginary part affects the amplitude for both the complex-order capacitor and complex-order memristor. More interesting is that the complex-order capacitor can do well at the time of fitting electrochemistry impedance spectra. The complex-order memristor is also analyzed. The area inside the hysteresis loops increases with the increasing of the imaginary part of the order and decreases with the increasing of the real part. Some complex case of complex-order memristors hysteresis loops are analyzed at last, whose loop has touching points beyond the origin of the coordinate system.

Key words: complex derivative, fractional-order elements, imaginary and real part, memristor

中图分类号:  (Nonlinear dynamics and chaos)

  • 05.45.-a
05.10.-a (Computational methods in statistical physics and nonlinear dynamics)