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

• 作 者: Gangquan Si Lijie Diao Jianwei Zhu Yuhang Lei Yanbin Zhang
• 机 构: State Key Laboratory of Electrical Insulation and Power Equipment, Xi’an Jiaotong University, Xi’an
• 出 处: 中国物理B（英文版）
• 发表日期: 2017年6期
• 关键词: complex derivative fractional-order elements imaginary and real part memristor

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 complexorder 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.