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Fractional-order charge-controlled memristor: theoretical analysis and simulation

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Abstract

Fractional calculus generalizes integer-order derivatives and integrals. Memristor represents the missing relation between the charge and flux among the conventional elements. This paper introduces the fractional calculus into charge-controlled memristor to establish a unified cubic fractional-order charge-controlled memristor model, which is more general and comprehensive, and the model is analyzed when the fractional-order \(\alpha \) change in the range of 0–1. Some interesting phenomena are found that the I–V characteristic is not the conventional double-loop I–V curves, but which can be called triple-loop I–V curves. The area inside the hysteresis loops decreases not only by the fractional-order \(\alpha \) decreasing, but also by the input frequency \(\omega \) increasing.

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Authors and Affiliations

  1. State Key Laboratory of Electrical Insulation and Power Equipment, School of Electrical Engineering, Xi’an Jiaotong University, Xi’an, 710049, Shaanxi Province, China

    Gangquan Si, Lijie Diao & Jianwei Zhu

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  1. Gangquan Si
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  2. Lijie Diao
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  3. Jianwei Zhu
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Correspondence to Gangquan Si.

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Si, G., Diao, L. & Zhu, J. Fractional-order charge-controlled memristor: theoretical analysis and simulation. Nonlinear Dyn 87, 2625–2634 (2017). https://doi.org/10.1007/s11071-016-3215-1

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