Please wait a minute...
Chin. Phys. B, 2022, Vol. 31(6): 060204    DOI: 10.1088/1674-1056/ac615c
Special Issue: SPECIAL TOPIC— Interdisciplinary physics: Complex network dynamics and emerging technologies
TOPICAL REVIEW—Interdisciplinary physics: Complex network dynamics and emerging technologies Prev   Next  

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
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.
Keywords:  fractional calculus      fractional-order memristor      fracmemristor      memristor  
Received:  01 July 2021      Revised:  10 March 2022      Accepted manuscript online:  28 March 2022
PACS:  02.30.Ik (Integrable systems)  
  07.07.Df (Sensors (chemical, optical, electrical, movement, gas, etc.); remote sensing)  
Fund: 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).
Corresponding Authors:  Yi-Fei Pu     E-mail:

Cite this article: 

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 2022 Chin. Phys. B 31 060204

[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
[1] Hopf bifurcation and phase synchronization in memristor-coupled Hindmarsh-Rose and FitzHugh-Nagumo neurons with two time delays
Zhan-Hong Guo(郭展宏), Zhi-Jun Li(李志军), Meng-Jiao Wang(王梦蛟), and Ming-Lin Ma(马铭磷). Chin. Phys. B, 2023, 32(3): 038701.
[2] An incommensurate fractional discrete macroeconomic system: Bifurcation, chaos, and complexity
Abderrahmane Abbes, Adel Ouannas, and Nabil Shawagfeh. Chin. Phys. B, 2023, 32(3): 030203.
[3] Memristor's characteristics: From non-ideal to ideal
Fan Sun(孙帆), Jing Su(粟静), Jie Li(李杰), Shukai Duan(段书凯), and Xiaofang Hu(胡小方). Chin. Phys. B, 2023, 32(2): 028401.
[4] Memristor hyperchaos in a generalized Kolmogorov-type system with extreme multistability
Xiaodong Jiao(焦晓东), Mingfeng Yuan(袁明峰), Jin Tao(陶金), Hao Sun(孙昊), Qinglin Sun(孙青林), and Zengqiang Chen(陈增强). Chin. Phys. B, 2023, 32(1): 010507.
[5] High-performance artificial neurons based on Ag/MXene/GST/Pt threshold switching memristors
Xiao-Juan Lian(连晓娟), Jin-Ke Fu(付金科), Zhi-Xuan Gao(高志瑄),Shi-Pu Gu(顾世浦), and Lei Wang(王磊). Chin. Phys. B, 2023, 32(1): 017304.
[6] Firing activities in a fractional-order Hindmarsh-Rose neuron with multistable memristor as autapse
Zhi-Jun Li(李志军), Wen-Qiang Xie(谢文强), Jin-Fang Zeng(曾金芳), and Yi-Cheng Zeng(曾以成). Chin. Phys. B, 2023, 32(1): 010503.
[7] High throughput N-modular redundancy for error correction design of memristive stateful logic
Xi Zhu(朱熙), Hui Xu(徐晖), Weiping Yang(杨为平), Zhiwei Li(李智炜), Haijun Liu(刘海军), Sen Liu(刘森), Yinan Wang(王义楠), and Hongchang Long(龙泓昌). Chin. Phys. B, 2023, 32(1): 018502.
[8] Design and FPGA implementation of a memristor-based multi-scroll hyperchaotic system
Sheng-Hao Jia(贾生浩), Yu-Xia Li(李玉霞), Qing-Yu Shi(石擎宇), and Xia Huang(黄霞). Chin. Phys. B, 2022, 31(7): 070505.
[9] Fabrication and investigation of ferroelectric memristors with various synaptic plasticities
Qi Qin(秦琦), Miaocheng Zhang(张缪城), Suhao Yao(姚苏昊), Xingyu Chen(陈星宇), Aoze Han(韩翱泽),Ziyang Chen(陈子洋), Chenxi Ma(马晨曦), Min Wang(王敏), Xintong Chen(陈昕彤), Yu Wang(王宇),Qiangqiang Zhang(张强强), Xiaoyan Liu(刘晓燕), Ertao Hu(胡二涛), Lei Wang(王磊), and Yi Tong(童祎). Chin. Phys. B, 2022, 31(7): 078502.
[10] Pulse coding off-chip learning algorithm for memristive artificial neural network
Ming-Jian Guo(郭明健), Shu-Kai Duan(段书凯), and Li-Dan Wang(王丽丹). Chin. Phys. B, 2022, 31(7): 078702.
[11] The dynamics of a memristor-based Rulkov neuron with fractional-order difference
Yan-Mei Lu(卢艳梅), Chun-Hua Wang(王春华), Quan-Li Deng(邓全利), and Cong Xu(徐聪). Chin. Phys. B, 2022, 31(6): 060502.
[12] Solutions and memory effect of fractional-order chaotic system: A review
Shaobo He(贺少波), Huihai Wang(王会海), and Kehui Sun(孙克辉). Chin. Phys. B, 2022, 31(6): 060501.
[13] Memristor-based multi-synaptic spiking neuron circuit for spiking neural network
Wenwu Jiang(蒋文武), Jie Li(李杰), Hongbo Liu(刘洪波), Xicong Qian(钱曦聪), Yuan Ge(葛源), Lidan Wang(王丽丹), and Shukai Duan(段书凯). Chin. Phys. B, 2022, 31(4): 040702.
[14] Complex dynamic behaviors in hyperbolic-type memristor-based cellular neural network
Ai-Xue Qi(齐爱学), Bin-Da Zhu(朱斌达), and Guang-Yi Wang(王光义). Chin. Phys. B, 2022, 31(2): 020502.
[15] A novel hyperchaotic map with sine chaotification and discrete memristor
Qiankun Sun(孙乾坤), Shaobo He(贺少波), Kehui Sun(孙克辉), and Huihai Wang(王会海). Chin. Phys. B, 2022, 31(12): 120501.
No Suggested Reading articles found!