A mathematical analysis: From memristor to fracmemristor

doi:10.1088/1674-1056/ac615c

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

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 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 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).

摘要/Abstract

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)

02.30.Ik

07.07.Df (Sensors (chemical, optical, electrical, movement, gas, etc.); remote sensing)

Wu-Yang Zhu(朱伍洋), Yi-Fei Pu(蒲亦非), Bo Liu(刘博), Bo Yu(余波), and Ji-Liu Zhou(周激流). A mathematical analysis: From memristor to fracmemristor[J]. 中国物理B, 2022, 31(6): 60204-060204.

Wu-Yang Zhu(朱伍洋), Yi-Fei Pu(蒲亦非), Bo Liu(刘博), Bo Yu(余波), and Ji-Liu Zhou(周激流). A mathematical analysis: From memristor to fracmemristor[J]. Chin. Phys. B, 2022, 31(6): 60204-060204.

参考文献

[1] Chua L O and Kang S M 1976 Proc. IEEE 64 209
[2] Chua L O 2003 IEEE Trans. Circuit Theory 18 507
[3] Strukov D B, Snider G S, Stewart D R and Williams R S 2008 Nature 453 80
[4] Calvin Coopmans 2009 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference. San Diego, California, USA 1127
[5] Chua L O 2012 Proc. IEEE 100 1920
[6] Xue W H, Ci W J, Xu X H and Liu G 2020 Chin. Phys. B 29 048401
[7] Shao N, Zhang S B and Shao S Y 2017 Chin. Phys. B 26 118501
[8] Yang B B, Xu N and Zhou E R 2020 Chin. Phys. B 29 048505
[9] Oldham K B and Spanier J 1973 The fractional calculus: Theory and applications of differentiation and integration to arbitrary order 1st Edition (Dover Publications)
[10] Podlubny I 2013 Math. Sci. Engineer. 2013 553
[11] Povstenko Y 2014 Fract. Calculus & Appl. Anal. 17 122
[12] Pu Y F 2016 IEEE Access 4 3398
[13] Pu Y F 2016 IEEE Access 4 3379
[14] Pu Y F, Yi Z and Zhou J L 2017 Int. J. Neural Sys. 27 1750003
[15] Pu Y F and Yuan X 2016 IEEE Access 4 1872
[16] Coopmans C, Pet I and Chen Y 2009 In ASME 2009 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference p. 1127
[17] Elsafty A H, Hamed E M, Fouda M E, Said L A and Radwan A G 2018 In 2018 7th International Conference on Modern Circuits and Systems Technologies (MOCAST)
[18] Fouda M E and Radwan A G 2013 J. Fract. Calculus Appl. 4 1
[19] Guo Z, Si G, Diao L, Jia L and Zhang Y 2017 Commun. Nonlinear Sci. Numer. Simulat. 59 177
[20] Khalil N A, Said L A, Radwan A G and Soliman A M 2019 Microelectronics J. 90 211
[21] Radwan A G, Moaddy K and Hashim I 2013 Abs. Appl. Anal. 758676
[22] Pu Y F, Yuan X and Yu B 2018 IEEE Transactions on Circuits and Systems I: Regular Papers 9 2903
[23] Pu Y F, Zhou J L and Yuan X 2010 IEEE T. Image Proce. 19 491
[24] Machado J T 2013 Communications in nonlinear Science and Numerical Simulation 2 264
[25] Cafagna D and Grassi G 2012 Nonlinear Dyn. 70 1185
[26] Itoh M and Chua L O 2008 Int. J. Bifurcation Chaos 18 3183
[27] Bao B C, Liu Z and Xu J P 2010 Chin. Phys. B 19 030510
[28] Bao B C, Jiang T, Wang G Y, Jin P P and Bao H 2019 Nonlinear Dyn. 89 1157
[29] Pu Y F, Zhou J L, Zhang Y, Zhang N, Huang G and Siarry P 2015 IEEE Trans. Neural Networks Learning Sys. 26 653
[30] Manabe S 2002 Nonlinear Dyn. 29 251
[31] Petras I 2010 IEEE Trans. Circuits & Sys. II-Exp. Briefs 57 975
[32] Wang Wu, Iu, Shen and Zhou 2019 Entropy 21 955
[33] Khalil N A, Fouda M E, Said L A, Radwan A G and Soliman A M 2020 In 2020 32nd International Conference on Microelectronics (ICM) Electr Network 226

A mathematical analysis: From memristor to fracmemristor

A mathematical analysis: From memristor to fracmemristor

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