中国物理B ›› 2022, Vol. 31 ›› Issue (6): 60204-060204.doi: 10.1088/1674-1056/ac615c

所属专题： SPECIAL TOPIC — Interdisciplinary physics: Complex network dynamics and emerging technologies

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A mathematical analysis: From memristor to fracmemristor

Wu-Yang Zhu(朱伍洋)1, Yi-Fei Pu(蒲亦非)1,†, Bo Liu(刘博)1, Bo Yu(余波)2, and Ji-Liu Zhou(周激流)3   

  1. 1 College of Computer Science, Sichuan University, Chengdu 610065, China;
    2 College of Physics and Engineering, Chengdu Normal University, Chengdu 611130, China;
    3 Chengdu University of Information Technology, Chengdu 610225, China
  • 收稿日期:2021-07-01 修回日期:2022-03-10 接受日期:2022-03-28 出版日期:2022-05-17 发布日期:2022-05-31
  • 通讯作者: Yi-Fei Pu E-mail:puyifei@scu.edu.cn
  • 基金资助:
    Project supported in part by the National Natural Science Foundation of China (Grant No. 62171303), China South Industries Group Corporation (Chengdu) Fire Control Technology Center Project (non-secret) (Grant No. HK20-03), and the National Key Research and Development Program Foundation of China (Grant No. 2018YFC0830300).

A mathematical analysis: From memristor to fracmemristor

Wu-Yang Zhu(朱伍洋)1, Yi-Fei Pu(蒲亦非)1,†, Bo Liu(刘博)1, Bo Yu(余波)2, and Ji-Liu Zhou(周激流)3   

  1. 1 College of Computer Science, Sichuan University, Chengdu 610065, China;
    2 College of Physics and Engineering, Chengdu Normal University, Chengdu 611130, China;
    3 Chengdu University of Information Technology, Chengdu 610225, China
  • Received:2021-07-01 Revised:2022-03-10 Accepted:2022-03-28 Online:2022-05-17 Published:2022-05-31
  • Contact: Yi-Fei Pu E-mail:puyifei@scu.edu.cn
  • Supported by:
    Project supported in part by the National Natural Science Foundation of China (Grant No. 62171303), China South Industries Group Corporation (Chengdu) Fire Control Technology Center Project (non-secret) (Grant No. HK20-03), and the National Key Research and Development Program Foundation of China (Grant No. 2018YFC0830300).

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摘要： The memristor is also a basic electronic component, just like resistors, capacitors and inductors. It is a nonlinear device with memory characteristics. In 2008, with HP's announcement of the discovery of the TiO2 memristor, the new memristor system, memory capacitor (memcapacitor) and memory inductor (meminductor) were derived. Fractional-order calculus has the characteristics of non-locality, weak singularity and long term memory which traditional integer-order calculus does not have, and can accurately portray or model real-world problems better than the classic integer-order calculus. In recent years, researchers have extended the modeling method of memristor by fractional calculus, and proposed the fractional-order memristor, but its concept is not unified. This paper reviews the existing memristive elements, including integer-order memristor systems and fractional-order memristor systems. We analyze their similarities and differences, give the derivation process, circuit schematic diagrams, and an outlook on the development direction of fractional-order memristive elements.

关键词: fractional calculus, fractional-order memristor, fracmemristor, memristor

Abstract: The memristor is also a basic electronic component, just like resistors, capacitors and inductors. It is a nonlinear device with memory characteristics. In 2008, with HP's announcement of the discovery of the TiO2 memristor, the new memristor system, memory capacitor (memcapacitor) and memory inductor (meminductor) were derived. Fractional-order calculus has the characteristics of non-locality, weak singularity and long term memory which traditional integer-order calculus does not have, and can accurately portray or model real-world problems better than the classic integer-order calculus. In recent years, researchers have extended the modeling method of memristor by fractional calculus, and proposed the fractional-order memristor, but its concept is not unified. This paper reviews the existing memristive elements, including integer-order memristor systems and fractional-order memristor systems. We analyze their similarities and differences, give the derivation process, circuit schematic diagrams, and an outlook on the development direction of fractional-order memristive elements.

Key words: fractional calculus, fractional-order memristor, fracmemristor, memristor

中图分类号:  (Integrable systems)

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