Design of novel memristor-based neuromorphic circuit and its application in classical conditioning

Xu Wei; Wang Yu-Qi; Li Yue-Feng; Gao Fei; Zhang Miao-Cheng; Lian Xiao-Juan; Wan Xiang; Xiao Jian; Tong Yi

doi:10.7498/aps.68.20191023

Abstract

Inspired by the working mechanism of human brain, the artificial neural network attracts great interest for its capability of parallel processing, which is favored by big data task. However, the electronic synapse based on CMOS neural network needs at least ten transistors to realize one biological synaptic function. So, CMOS-based neural network exhibits obvious weakness in speed, power consumption, circuit area and resource utilization and so on, compared with biological synapses. Therefore, how to build neuromorphic circuits and realize biological functions by constructing electronic synapses with low power consumption and high integration density have become the key points for human to realize brain-like computing system. Memristors, as the fourth basic component, is a two-terminal nonlinear device possessing nonlinear conductance that can be tuned continuously. For that special characteristic, it is very similar to biological synapse whose connection strength can be adjusted continuously. In this article, first of all, we study the electrical characteristic of the Cu/MXene/SiO₂/W memristor. When applying a positive DC sweeping voltage to the Cu electrode, the Cu electrode is oxidized, generating Cu²⁺. The generated Cu²⁺ in function layer tends tomove towards the bottom electrode under the action of electric field. Near the bottom electrode the Cu²⁺ moving from top electrode are reduced, generating a conductive Cu atom. With Cu atoms accumulating and extending from bottom electrode to top electrode, the memristor is gradually converted from the initial high resistance state (HRS) into the low resistance state (LRS). Secondly, combining with HP model of memristor, we utilize Verilog A language to simulate memristor in the experiment we conducted. Subsequently, we successfully construct the artificial synaptic unit and design the weight differential circuit with self-feedback branch. In the above circuit, we successfully implementa classical " Pavlov's dog” experiment. By applying the sinusoidal signal and pulse signal to the synaptic unit for testing and training it, respectively, the circuit realizes the convention between the conditions that unconditioned stimulus producing unconditioned response to conditioned stimulus producing conditions response. This work takes memristor as a center, through modelling the electrical characteristic of Cu/MXene/ SiO₂/W device, we construct a neuromorphic circuit with weight differential branch andself-feedback branch, successfully simulate the classical learning behavior of biological synapses, and realizes the whole process of biologically conditioned reflex, which is illustrated in detail in the experiment on " Pavlov′s dog”. The results will provide effective guidance forconstructing a large scale and high density neuromorphic circuitbased on memristor, thus promoting the realization of brain-like computation in the future.

Keywords:

Authors and contacts

College of Electronic and Optical Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210023, China

Corresponding author: Xiao Jian, xiaoj@njupt.edu.cn ; Tong Yi, tongyi@njupt.edu.cn

Funds: Project supported by the Jiangsu Specially-Appointed Professor and the Science Research Funds for Nanjing University of Posts and Telecommunications, China (Grant Nos. SZDG20180007, NY217116, KFJJ20170101, NY219014, NY218110), the China Postdoctoral Science Foundation (Grant No. 2018M642290), the National Natural Science Foundation of China (Grant No. 61804079), the University Natural Science Foundation of Jiangsu Province, China (Grant No.18KJD510005), the Innovative Doctor Program, China (Grant Nos. CZ1060619001), and the Graduate Research and Innovation Projects of Jiangsu Province, China (Grant Nos. SJCX19_0256, SJKY19_0811, SJKY19_0806)

FullText HTML : translate this paragraph

References

[1]	Backus J 1978 Commun. ACM 21 513
[2]	Wang J, Zhuge F 2019 Adv. Mater. Technol. 4 1800544 Google Scholar
[3]	Murre J M, Sturdy D P 1995 Biol. Cybern. 73 529 Google Scholar
[4]	Braitenberg V, Schuz A A 1991 J. Anat. 179 203
[5]	Sporns O, Tononi G, Kötter R 2005 PLoS Comput. Biol. 1 42 Google Scholar
[6]	Hebb D O 1949 Am. J. Psychol. 63 633
[7]	Wixted J T, Ebbesen E B 1991 Psychol. Sci. 2 409 Google Scholar
[8]	Douglas R, Mahowald M, Mead C 1995 Annu. Rev. Neurosci. 18 255 Google Scholar
[9]	Jürgen S 2015 Neural Networks 61 85 Google Scholar
[10]	Dean J, Corrado G S, Monga R, Chen K, Devin M, Le Q V, Mao M Z, Ranzato M A, Senior A, Tucker P, Yang K, Ng A Y 2012 Advances in Neural Information Processing Systems Harrahs and Harveys, Lake Tahoe, December 3–8, 2012 p1232
[11]	Rachmuth G, Poon C S 2008 Hfsp Journal 2 156 Google Scholar
[12]	Liu Y H, Zhu L Q, Feng P, Shi Y, Wan Q 2015 Adv. Mater. 27 5599 Google Scholar
[13]	Lont J B, Guggenbuhl W 1992 IEEE Trans. Neural Networks 3 457 Google Scholar
[14]	Dmitri B S, Gregory S S, Duncan R S, Williams R S 2008 Nature 453 80 Google Scholar
[15]	Jeong H, Shi L P 2019 J. Phys. D: Appl. Phys. 52 023003 Google Scholar
[16]	Waser R, Aono M 2007 Nat. Mater. 6 833 Google Scholar
[17]	Hirose Y, Hirose H 1976 J. Appl. Phys. 47 2767 Google Scholar
[18]	余志强, 刘敏丽, 郎建勋, 钱楷, 张昌华 2018 67 157302 Google Scholar Yu Z Q, Liu M L, Lang J X, Qian K, Zhang C H 2018 Acta Phys. Sin. 67 157302 Google Scholar
[19]	Hui Q H, Zhao L, Wang X P 2019 Neurocomputing 330 11 Google Scholar
[20]	Daniele I 2016 Semicond. Sci. Technol. 31 063002 Google Scholar
[21]	Wu L, Liu H X, Li J B, Wang S L, Wang X 2019 Nanoscale Res. Lett. 14 184 Google Scholar
[22]	Gurme S T, Dongale T D, Surwase S N, Kumbhar S D, More G M, Pati V L, Patil P S, Kamat R K, Jadhav J P 2018 Phys. Status Solidi. 215 1800550 Google Scholar
[23]	Ling Z, Ren C E, Zhao M Q, Yang J, Giammarco J M, Qiu J, Barsoum M W Gogotsi Y 2014 PNAS 111 16676 Google Scholar
[24]	Lei J C, Zhang X, Zhou Z, Lei J C, Zhang X, Zhou Z 2015 Front. Phys. Beijing 10 276 Google Scholar
[25]	Yan X B, Wang K Y, Zhao J H, Zhou Z Y, Wang H, Wang J J, Zhang L, Li X Y, Xiao Z A, Zhao Q L, Pei Y F, Wang G, Qin C Y, Li H, Lou J Z, Liu Q, Zhou P 2019 Small 15 1900107 Google Scholar
[26]	Li D, Wu B, Zhu X, Wang J, Ryu B, Lu W D, Lu W, Liang X 2018 ACS Nano 12 9240 Google Scholar
[27]	Zhou L, Yang S W, Ding G Q, Yang J Q, Ren Y, Zhang S R, Mao J Y, Yang Y C, Zhou Y, Han S T 2019 Nano Energy 58 293 Google Scholar
[28]	Radtke P K, Schimansky G L 2016 AIP Adv. 6 055119 Google Scholar
[29]	Dickinson A 1981 Br. Med. Bull. 37 165 Google Scholar
[30]	Zhang M C, Wang Y Q, Gao F, Wang Y, Shen X Y, He N, Zhu J L, Chen Y H, Wan X, Lian X J, Hu E T, Xu J G, Tong Y 2019 Ceram. Int. 45 19467 Google Scholar
[31]	陈义豪, 徐威, 王钰琪, 万相, 李岳峰, 梁定康, 陆立群, 刘鑫伟, 连晓娟, 胡二涛, 郭宇锋, 许剑光, 童祎, 肖建 2019 68 098501 Google Scholar Chen Y H, Xu W, Wang Y Q, Wan X, Li Y F, Liang D K, Lu L Q, Liu X W, Lian X J, Hu E T, Guo Y F, Xu J G, Tong Y, Xiao J 2019 Acta Phys. Sin. 68 098501 Google Scholar
[32]	McAndrew C C, Coram G J, Gullapalli K K, Jones J B, Nagel L W, Roy A S, Roychowdhury J, Scholten A J, Smit G D J, Wang X, Yoshitomi S 2017 IEEE J. Electron Dev. 3 383
[33]	Messaris I, Serb A, Stathopoulos S, Khiat A, Nikolaidis S, Prodromakis T 2018 IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 37 3151 Google Scholar
[34]	McDonald N R, Pino R E, Rozwood P J, Wysocki B T 2010 IEEE International Joint Conference on Neural Networks Barcelona, Spain, July 18–23, 2010 p1
[35]	Dongale T D, Patil P J, Desai N K, Chougule P P, Kumbhar S M, Waifalkar P P, Patil P B, Vhatkar R S, Takale M V, Gaikwad P K, Kamat R K 2016 Nano Convergence 3 16 Google Scholar
[36]	Hu X, Feng G, Duan S, Liu L 2016 IEEE T. Neur. Net. Lear. 28 1889
[37]	Zhao J, Zhou Z, Zhang Y, Wang J, Zhang L, Li X, Zhao M, Wang H, Pei Y, Zhao Q, Xiao Z, Wang K, Qin C, Wang G, Li H, Ding B, Yan F, Wang K, Ren D, Liu B, Yan X 2019 J. Mater. Chem. C 7 1298 Google Scholar
[38]	Pan Y, Wan T, Du H, Qu B, Wang D, Ha T J, Chu D 2018 J. Alloys Compd. 757 496 Google Scholar
[39]	Hong X L, Loy J J, Dananjaya P A, Tan F, Ng C M, Lew W S 2018 J. Mater. Sci. 53 8720 Google Scholar
[40]	Wan X, Liang D K, Gao Fei, Lian X J, Tong Y 2018 Appl. Phys. Express 11 114601 Google Scholar
[41]	Yakopcic C, Tarek T M 2018 International Joint Conference on Neural Networks Rio de Janeiro, Brazil, July 8–13, 2018 p8489252

Cited By

图 1 (a) Cu/MXene/SiO₂/W忆阻器结构及电学测试示意图; (b)二维材料MXene的扫描电镜图; (b) 金相显微镜下忆阻器表面结构; (d)正向偏压下器件工作机理示意图; (e)受到刺激信号, 突触前膜、突触后膜之间神经递质迁移示意图

Figure 1. (a) The device structure and measurement of Cu/MXene/SiO₂/W memristor; (b) surface structure of memristor under metallographic microscope; (c) the scanning electron microscope result of two-dimensional material MXene; (d) the physical mechanism of the Cu/MXene/SiO₂/W memristor under positive voltagestimulus; (e) the neurotransmitter transfer between pre- and postsynaptic membrane after stimulus.

DownLoad: Full-Size Img PowerPoint

图 2 (a)惠普研究小组提出的忆阻器模型; (b)忆阻器模型仿真数据与实验测试数据拟合

Figure 2. (a) Memristor model reported by HP group; (b) the fitting of experimental data and the simulation data.

DownLoad: Full-Size Img PowerPoint

图 3 实现条件反射的神经形态电路

Figure 3. Neuromorphic circuitry for the emulation of classical conditioning.

DownLoad: Full-Size Img PowerPoint

图 4 (a)仿真过程施加的信号以及各自对应的结果图; (b)对电路中忆阻器模型进行直流电压扫描, 流经忆阻器的电流随仿真时间的变化; (c)训练过程中, 流经忆阻器M_a的电流随时间的变化

Figure 4. (a) The signals inputted into the circuit and corresponding output waveform, respectively; (b) the change of current flowing through the memristor against timeduring DC voltage sweeping; (c) the change of current through the memristor M_a during training process.

DownLoad: Full-Size Img PowerPoint

表 1 模型主要参数

Table 1. Key modeling parameters.

开启电阻	截止电阻	有源区长度	离子迁移率	窗函数参数
${R_{{\rm{on}}}}/\Omega $	${R_{{\rm{off}}}}/\Omega $	D/m	u_v	x₀	y₀	p	m
3.7 × 10²	1.9 × 10⁴	3.0 × 10^–8	3.0 × 10^–13	0.3	0.7	30	100

DownLoad: CSV

map

[1]	Backus J 1978 Commun. ACM 21 513
[2]	Wang J, Zhuge F 2019 Adv. Mater. Technol. 4 1800544 Google Scholar
[3]	Murre J M, Sturdy D P 1995 Biol. Cybern. 73 529 Google Scholar
[4]	Braitenberg V, Schuz A A 1991 J. Anat. 179 203
[5]	Sporns O, Tononi G, Kötter R 2005 PLoS Comput. Biol. 1 42 Google Scholar
[6]	Hebb D O 1949 Am. J. Psychol. 63 633
[7]	Wixted J T, Ebbesen E B 1991 Psychol. Sci. 2 409 Google Scholar
[8]	Douglas R, Mahowald M, Mead C 1995 Annu. Rev. Neurosci. 18 255 Google Scholar
[9]	Jürgen S 2015 Neural Networks 61 85 Google Scholar
[10]	Dean J, Corrado G S, Monga R, Chen K, Devin M, Le Q V, Mao M Z, Ranzato M A, Senior A, Tucker P, Yang K, Ng A Y 2012 Advances in Neural Information Processing Systems Harrahs and Harveys, Lake Tahoe, December 3–8, 2012 p1232
[11]	Rachmuth G, Poon C S 2008 Hfsp Journal 2 156 Google Scholar
[12]	Liu Y H, Zhu L Q, Feng P, Shi Y, Wan Q 2015 Adv. Mater. 27 5599 Google Scholar
[13]	Lont J B, Guggenbuhl W 1992 IEEE Trans. Neural Networks 3 457 Google Scholar
[14]	Dmitri B S, Gregory S S, Duncan R S, Williams R S 2008 Nature 453 80 Google Scholar
[15]	Jeong H, Shi L P 2019 J. Phys. D: Appl. Phys. 52 023003 Google Scholar
[16]	Waser R, Aono M 2007 Nat. Mater. 6 833 Google Scholar
[17]	Hirose Y, Hirose H 1976 J. Appl. Phys. 47 2767 Google Scholar
[18]	余志强, 刘敏丽, 郎建勋, 钱楷, 张昌华 2018 67 157302 Google Scholar Yu Z Q, Liu M L, Lang J X, Qian K, Zhang C H 2018 Acta Phys. Sin. 67 157302 Google Scholar
[19]	Hui Q H, Zhao L, Wang X P 2019 Neurocomputing 330 11 Google Scholar
[20]	Daniele I 2016 Semicond. Sci. Technol. 31 063002 Google Scholar
[21]	Wu L, Liu H X, Li J B, Wang S L, Wang X 2019 Nanoscale Res. Lett. 14 184 Google Scholar
[22]	Gurme S T, Dongale T D, Surwase S N, Kumbhar S D, More G M, Pati V L, Patil P S, Kamat R K, Jadhav J P 2018 Phys. Status Solidi. 215 1800550 Google Scholar
[23]	Ling Z, Ren C E, Zhao M Q, Yang J, Giammarco J M, Qiu J, Barsoum M W Gogotsi Y 2014 PNAS 111 16676 Google Scholar
[24]	Lei J C, Zhang X, Zhou Z, Lei J C, Zhang X, Zhou Z 2015 Front. Phys. Beijing 10 276 Google Scholar
[25]	Yan X B, Wang K Y, Zhao J H, Zhou Z Y, Wang H, Wang J J, Zhang L, Li X Y, Xiao Z A, Zhao Q L, Pei Y F, Wang G, Qin C Y, Li H, Lou J Z, Liu Q, Zhou P 2019 Small 15 1900107 Google Scholar
[26]	Li D, Wu B, Zhu X, Wang J, Ryu B, Lu W D, Lu W, Liang X 2018 ACS Nano 12 9240 Google Scholar
[27]	Zhou L, Yang S W, Ding G Q, Yang J Q, Ren Y, Zhang S R, Mao J Y, Yang Y C, Zhou Y, Han S T 2019 Nano Energy 58 293 Google Scholar
[28]	Radtke P K, Schimansky G L 2016 AIP Adv. 6 055119 Google Scholar
[29]	Dickinson A 1981 Br. Med. Bull. 37 165 Google Scholar
[30]	Zhang M C, Wang Y Q, Gao F, Wang Y, Shen X Y, He N, Zhu J L, Chen Y H, Wan X, Lian X J, Hu E T, Xu J G, Tong Y 2019 Ceram. Int. 45 19467 Google Scholar
[31]	陈义豪, 徐威, 王钰琪, 万相, 李岳峰, 梁定康, 陆立群, 刘鑫伟, 连晓娟, 胡二涛, 郭宇锋, 许剑光, 童祎, 肖建 2019 68 098501 Google Scholar Chen Y H, Xu W, Wang Y Q, Wan X, Li Y F, Liang D K, Lu L Q, Liu X W, Lian X J, Hu E T, Guo Y F, Xu J G, Tong Y, Xiao J 2019 Acta Phys. Sin. 68 098501 Google Scholar
[32]	McAndrew C C, Coram G J, Gullapalli K K, Jones J B, Nagel L W, Roy A S, Roychowdhury J, Scholten A J, Smit G D J, Wang X, Yoshitomi S 2017 IEEE J. Electron Dev. 3 383
[33]	Messaris I, Serb A, Stathopoulos S, Khiat A, Nikolaidis S, Prodromakis T 2018 IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 37 3151 Google Scholar
[34]	McDonald N R, Pino R E, Rozwood P J, Wysocki B T 2010 IEEE International Joint Conference on Neural Networks Barcelona, Spain, July 18–23, 2010 p1
[35]	Dongale T D, Patil P J, Desai N K, Chougule P P, Kumbhar S M, Waifalkar P P, Patil P B, Vhatkar R S, Takale M V, Gaikwad P K, Kamat R K 2016 Nano Convergence 3 16 Google Scholar
[36]	Hu X, Feng G, Duan S, Liu L 2016 IEEE T. Neur. Net. Lear. 28 1889
[37]	Zhao J, Zhou Z, Zhang Y, Wang J, Zhang L, Li X, Zhao M, Wang H, Pei Y, Zhao Q, Xiao Z, Wang K, Qin C, Wang G, Li H, Ding B, Yan F, Wang K, Ren D, Liu B, Yan X 2019 J. Mater. Chem. C 7 1298 Google Scholar
[38]	Pan Y, Wan T, Du H, Qu B, Wang D, Ha T J, Chu D 2018 J. Alloys Compd. 757 496 Google Scholar
[39]	Hong X L, Loy J J, Dananjaya P A, Tan F, Ng C M, Lew W S 2018 J. Mater. Sci. 53 8720 Google Scholar
[40]	Wan X, Liang D K, Gao Fei, Lian X J, Tong Y 2018 Appl. Phys. Express 11 114601 Google Scholar
[41]	Yakopcic C, Tarek T M 2018 International Joint Conference on Neural Networks Rio de Janeiro, Brazil, July 8–13, 2018 p8489252

[1]	Wu Chao-Jun, Fang Li-Yi, Yang Ning-Ning. Dynamic analysis and experiment of chaotic circuit of non-homogeneous fractional memristor with bias voltage source. Acta Physica Sinica, 2024, 73(1): 010501. doi: 10.7498/aps.73.20231211
[2]	Wang Xuan, Du Jian-Rong, Li Zhi-Jun, Ma Ming-Lin, Li Chun-Lai. Coexisting discharge and synchronization of heterogeneous discrete neural network with crosstalk memristor synapses. Acta Physica Sinica, 2024, 73(11): 110503. doi: 10.7498/aps.73.20231972
[3]	Chen Kai-Hui, Fan Zhen, Dong Shuai, Li Wen-Jie, Chen Yi-Hong, Tian Guo, Chen De-Yang, Qin Ming-Hui, Zeng Min, Lu Xu-Bing, Zhou Guo-Fu, Gao Xing-Sen, Liu Jun-Ming. Perovskite-phase interfacial intercalated layer-induced performance enhancement in SrFeO_x-based memristors. Acta Physica Sinica, 2023, 72(9): 097301. doi: 10.7498/aps.72.20221934
[4]	Guo Hui-Meng, Liang Yan, Dong Yu-Jiao, Wang Guang-Yi. Simplification of Chua corsage memristor and hardware implementation of its neuron circuit. Acta Physica Sinica, 2023, 72(7): 070501. doi: 10.7498/aps.72.20222013
[5]	Wang Shi-Chang, Lu Zhen-Zhou, Liang Yan, Wang Guang-Yi. Neuromorphic behaviors of N-type locally-active memristor. Acta Physica Sinica, 2022, 71(5): 050502. doi: 10.7498/aps.71.20212017
[6]	Zhang Yu-Qi, Wang Jun-Jie, Lü Zi-Yu, Han Su-Ting. Multimode modulated memristors for in-sensor computing system. Acta Physica Sinica, 2022, 71(14): 148502. doi: 10.7498/aps.71.20220226
[7]	Wen Xin-Yu, Wang Ya-Sai, He Yu-Hui, Miao Xiang-Shui. Memristive brain-like computing. Acta Physica Sinica, 2022, 71(14): 140501. doi: 10.7498/aps.71.20220666
[8]	Chen Yi-Hao, Xu Wei, Wang Yu-Qi, Wan Xiang, Li Yue-Feng, Liang Ding-Kang, Lu Li-Qun, Liu Xin-Wei, Lian Xiao-Juan, Hu Er-Tao, Guo Yu-Feng, Xu Jian-Guang, Tong Yi, Xiao Jian. Fabrication of synaptic memristor based on two-dimensional material MXene and realization of both long-term and short-term plasticity. Acta Physica Sinica, 2019, 68(9): 098501. doi: 10.7498/aps.68.20182306
[9]	Liu Yi-Chun, Lin Ya, Wang Zhong-Qiang, Xu Hai-Yang. Oxide-based memristive neuromorphic synaptic devices. Acta Physica Sinica, 2019, 68(16): 168504. doi: 10.7498/aps.68.20191262
[10]	Wang Wei, Zeng Yi-Cheng, Sun Rui-Ting. Research on a six-order chaotic circuit with three memristors. Acta Physica Sinica, 2017, 66(4): 040502. doi: 10.7498/aps.66.040502
[11]	Shao Nan, Zhang Sheng-Bing, Shao Shu-Yuan. Modification of memristor model with synaptic characteristics and mechanism analysis of the model's learning-experience behavior. Acta Physica Sinica, 2016, 65(12): 128503. doi: 10.7498/aps.65.128503
[12]	Ruan Jing-Ya, Sun Ke-Hui, Mou Jun. Memristor-based Lorenz hyper-chaotic system and its circuit implementation. Acta Physica Sinica, 2016, 65(19): 190502. doi: 10.7498/aps.65.190502
[13]	Yu Ya-Juan, Wang Zai-Hua. A fractional-order memristor model and the fingerprint of the simple series circuits including a fractional-order memristor. Acta Physica Sinica, 2015, 64(23): 238401. doi: 10.7498/aps.64.238401
[14]	Meng Fan-Yi, Duan Shu-Kai, Wang Li-Dan, Hu Xiao-Fang, Dong Zhe-Kang. An improved WOx memristor model with synapse characteristic analysis. Acta Physica Sinica, 2015, 64(14): 148501. doi: 10.7498/aps.64.148501
[15]	Hong Qing-Hui, Li Zhi-Jun, Zeng Jin-Fang, Zeng Yi-Cheng. Design and simulation of a memristor chaotic circuit based on current feedback op amp. Acta Physica Sinica, 2014, 63(18): 180502. doi: 10.7498/aps.63.180502
[16]	Yang Fang-Yan, Leng Jia-Li, Li Qing-Du. The 4-dimensional hyperchaotic memristive circuit based on Chua’s circuit. Acta Physica Sinica, 2014, 63(8): 080502. doi: 10.7498/aps.63.080502
[17]	Liu Yu-Dong, Wang Lian-Ming. Application of memristor-based spiking neural network in image edge extraction. Acta Physica Sinica, 2014, 63(8): 080503. doi: 10.7498/aps.63.080503
[18]	Li Zhi-Jun, Zeng Yi-Cheng, Li Zhi-Bin. Memristive chaotic circuit based on modified SC-CNNs. Acta Physica Sinica, 2014, 63(1): 010502. doi: 10.7498/aps.63.010502
[19]	Liang Yan, Yu Dong-Sheng, Chen Hao. A novel meminductor emulator based on analog circuits. Acta Physica Sinica, 2013, 62(15): 158501. doi: 10.7498/aps.62.158501
[20]	Bao Bo-Cheng, Hu Wen, Xu Jian-Ping, Liu Zhong, Zou Ling. Analysis and implementation of memristor chaotic circuit. Acta Physica Sinica, 2011, 60(12): 120502. doi: 10.7498/aps.60.120502

Catalog

Vol. 68, Issue 23 - 2019-12-05

Metrics

Abstract views: 13151
PDF Downloads: 321
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板