Dimensionality reduction modeling and characteristic analysis of memristive circuit

Bao Bo-Cheng; Wang Chun-Li; Wu Hua-Gan; Qiao Xiao-Hua

doi:10.7498/aps.63.020504

Abstract

Through mathematical modeling analysis of Chua’s memristive circuit, the problem of dimensionality reduction for dynamical modeling of memristive circuit is proposed. Taking memristive circuit with two memristors for example, dimensionality reduction modeling of the memristive circuit is performed, on which a three-dimensional system model is established. Based on this model, the equilibrium points and stabilities are analyzed, and the dynamical characteristics, when the parameters are varied, are investigated. Furthermore, the analysis results from the conventional model are compared with the results from the dimensionality reduction model of memristive cicuit with two memristors. The results indicate that the dimensionality of the dimensionality reduction model of memristive circuit is related to the number of capacitors and inductors only, but unrelated to the number of memristors; there exist nonlinear phenomena about the coexistence of bifurcation modes in the memristive circuit when circuit parameters are varied; the dimensionality reduction modeling reduces the complexity of system modeling, which is conducive to dynamical charateristic analysis of the system but eliminates the effect of the initial conditions of the memristors internal state variables on dynamical charateristics of memristive circuit.

Keywords:

Authors and contacts

1.
School of Information Science and Engineering, Changzhou University, Changzhou 213164, China;
2.
Department of Electronic Engineering, Nanjing University of Science and Technology, Nanjing 210094, China;
3.
School of Electrical and Information Engineering, Jiangsu University of Technology, Changzhou 213001, China
Funds: Project supported by the National Natural Science Foundation of China (Grant No. 51277017) and the Natural Science Foundation of Jiangsu Province, China (Grant No. BK2012583).

References

[1]	Bao B C, Yang P, Ma Z H, Zhang X 2012 Acta Phys. Sin. 61 220502 (in Chinese) [包伯成, 杨平, 马正华, 张希 2012 物理学报 61 220502]
[2]	Yang P, Xu J P, He S Z, Bao B C 2013 Acta Phys. Sin. 62 160501 (in Chinese) [杨平, 许建平, 何圣仲, 包伯成 2013 物理学报 62 160501]
[3]	Bao B C, Zhou G H, Xu J P, Liu Z 2010 Acta Phys. Sin. 59 3769 (in Chinese) [包伯成, 周国华, 许建平, 刘中 2010 物理学报 59 3769]
[4]	Lu Y L, Jiang G P, Song Y R 2013 Acta Phys. Sin. 62 130202 (in Chinese) [鲁延玲, 蒋国平, 宋玉蓉 2013 物理学报 62 130202]
[5]	Zhao J, Yu L, Li J R 2013 Acta Phys. Sin. 62 130201 (in Chinese) [赵佳, 喻莉, 李静茹 2013 物理学报 62 130201]
[6]	Strukov D B, Snider G S, Stewart D R, Williams R S 2008 Nature 453 80
[7]	Borghetti J, Snider G S, Kuekes P J, Yang J J, Stewart D R, Williams R S 2010 Nature 464 873
[8]	Pershin Y V, Fontaine S L, Di Ventra M 2009 Phys. Rev. E 80 021926
[9]	Wu A L, Zeng Z G 2012 Neural Networks 36 1
[10]	Shin S, Kim K, Kang S M 2011 IEEE Trans. Nanotechnol. 10 266
[11]	Witrisal K 2009 Electron. Lett. 45 713
[12]	Bao B C, Feng F, Dong W, Pan S H 2013 Chin. Phys. B 22 068401
[13]	Li Z J, Zeng Y C 2013 Chin. Phys. B 22 040502
[14]	Bao B C, Xu J P, Liu Z 2010 Chin. Phys. Lett. 27 070504
[15]	Bao B C, Liu Z, Xu J P 2010 Acta Phys. Sin. 59 3785 (in Chinese) [包伯成, 刘中, 许建平 2010 物理学报 59 3785]
[16]	Bao B C, Hu W, Xu J P, Liu Z, Zou L 2011 Acta Phys. Sin. 60 120502 (in Chinese) [包伯成, 胡文, 许建平, 刘中, 邹凌 2011 物理学报 60 120502]
[17]	Bao B C, Liu Z, Xu J P 2010 Chin. Phys. B 19 030510
[18]	Bao B C, Xu J P, Zhou G H, Ma Z H, Zou L 2011 Chin. Phys. B 20 120502
[19]	Bao B C, Shi G D, Xu J P, Liu Z, Pan S H 2011 Sci. China: Tech. Sci. 54 2180
[20]	El-Sayed A M A, Elsaid A, Nour H M, Elsonbaty A 2013 Commun. Nonlinear Sci. Numer. Simulat. 18 148
[21]	Bao B C, Liu Z, Xu J P 2010 Electron. Lett. 46 237
[22]	Tsuneda A 2005 Int. J. Bifur. Chaos 15 1
[23]	Meng J D, Bao B C, Xu Q 2011 Acta Phys. Sin. 60 010504 (in Chinese) [孟继德, 包伯成, 徐强 2011 物理学报 60 010504]
[24]	Zhang X F, Chen Z Y, Ji Y, Bi Q S 2009 Chin. J. Theor. Appl. Mech. 41 765 (in Chinese) [张晓芳, 陈章耀, 季颖, 毕勤胜 2009 力学学报 41 765]
[25]	Chua L O 2011 Appl. Phys. A 102 765
[26]	Wang F 2013 IEEE Trans. Circuits Syst. I 60 616

Cited By

[1]	Bao B C, Yang P, Ma Z H, Zhang X 2012 Acta Phys. Sin. 61 220502 (in Chinese) [包伯成, 杨平, 马正华, 张希 2012 物理学报 61 220502]
[2]	Yang P, Xu J P, He S Z, Bao B C 2013 Acta Phys. Sin. 62 160501 (in Chinese) [杨平, 许建平, 何圣仲, 包伯成 2013 物理学报 62 160501]
[3]	Bao B C, Zhou G H, Xu J P, Liu Z 2010 Acta Phys. Sin. 59 3769 (in Chinese) [包伯成, 周国华, 许建平, 刘中 2010 物理学报 59 3769]
[4]	Lu Y L, Jiang G P, Song Y R 2013 Acta Phys. Sin. 62 130202 (in Chinese) [鲁延玲, 蒋国平, 宋玉蓉 2013 物理学报 62 130202]
[5]	Zhao J, Yu L, Li J R 2013 Acta Phys. Sin. 62 130201 (in Chinese) [赵佳, 喻莉, 李静茹 2013 物理学报 62 130201]
[6]	Strukov D B, Snider G S, Stewart D R, Williams R S 2008 Nature 453 80
[7]	Borghetti J, Snider G S, Kuekes P J, Yang J J, Stewart D R, Williams R S 2010 Nature 464 873
[8]	Pershin Y V, Fontaine S L, Di Ventra M 2009 Phys. Rev. E 80 021926
[9]	Wu A L, Zeng Z G 2012 Neural Networks 36 1
[10]	Shin S, Kim K, Kang S M 2011 IEEE Trans. Nanotechnol. 10 266
[11]	Witrisal K 2009 Electron. Lett. 45 713
[12]	Bao B C, Feng F, Dong W, Pan S H 2013 Chin. Phys. B 22 068401
[13]	Li Z J, Zeng Y C 2013 Chin. Phys. B 22 040502
[14]	Bao B C, Xu J P, Liu Z 2010 Chin. Phys. Lett. 27 070504
[15]	Bao B C, Liu Z, Xu J P 2010 Acta Phys. Sin. 59 3785 (in Chinese) [包伯成, 刘中, 许建平 2010 物理学报 59 3785]
[16]	Bao B C, Hu W, Xu J P, Liu Z, Zou L 2011 Acta Phys. Sin. 60 120502 (in Chinese) [包伯成, 胡文, 许建平, 刘中, 邹凌 2011 物理学报 60 120502]
[17]	Bao B C, Liu Z, Xu J P 2010 Chin. Phys. B 19 030510
[18]	Bao B C, Xu J P, Zhou G H, Ma Z H, Zou L 2011 Chin. Phys. B 20 120502
[19]	Bao B C, Shi G D, Xu J P, Liu Z, Pan S H 2011 Sci. China: Tech. Sci. 54 2180
[20]	El-Sayed A M A, Elsaid A, Nour H M, Elsonbaty A 2013 Commun. Nonlinear Sci. Numer. Simulat. 18 148
[21]	Bao B C, Liu Z, Xu J P 2010 Electron. Lett. 46 237
[22]	Tsuneda A 2005 Int. J. Bifur. Chaos 15 1
[23]	Meng J D, Bao B C, Xu Q 2011 Acta Phys. Sin. 60 010504 (in Chinese) [孟继德, 包伯成, 徐强 2011 物理学报 60 010504]
[24]	Zhang X F, Chen Z Y, Ji Y, Bi Q S 2009 Chin. J. Theor. Appl. Mech. 41 765 (in Chinese) [张晓芳, 陈章耀, 季颖, 毕勤胜 2009 力学学报 41 765]
[25]	Chua L O 2011 Appl. Phys. A 102 765
[26]	Wang F 2013 IEEE Trans. Circuits Syst. I 60 616

[1]	Ying Yao-Jun, Li Hai-Bin. Dynamics of Bose-Einstein condensation in an asymmetric double-well potential. Acta Physica Sinica, 2023, 72(13): 130303. doi: 10.7498/aps.72.20230419
[2]	Gao Yi-Wen, Wang Ying, Tian Wen-De, Chen Kang. Dynamic behavior of active polymer chain in spatially-modulated driven field. Acta Physica Sinica, 2022, 71(24): 240501. doi: 10.7498/aps.71.20221367
[3]	Xu Xiang, Zhu Cheng, Zhu Xian-Qiang. Discrete data based local-to-global network reconstruction algorithm. Acta Physica Sinica, 2021, 70(8): 088901. doi: 10.7498/aps.70.20201756
[4]	He Ren, Li Ying-Ye, Chen Jing-Xin, Zhao Xue-Ling, Tang Huan, Zhang Li-Na, Shen Yan-Jiao, Li Feng, Yang Lin, Wei De-Yuan. Three-point and four-point mechanical bending test modeling and application in solar cells. Acta Physica Sinica, 2019, 68(20): 208801. doi: 10.7498/aps.68.20190597
[5]	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
[6]	Xia Xiao-Fei, Wang Jun-Song. Influence of synaptic plasticity on dynamics of neural mass model：a bifurcation study. Acta Physica Sinica, 2014, 63(14): 140503. doi: 10.7498/aps.63.140503
[7]	He Sheng-Zhong, Zhou Guo-Hua, Xu Jian-Ping, Wu Song-Rong, Chen Li. Effect of output capacitance time-constant on dynamic characteristics of V2-controlled buck converter. Acta Physica Sinica, 2014, 63(13): 130501. doi: 10.7498/aps.63.130501
[8]	Xu Zhi-Cheng, Zhong Wei-Rong. Transient kinetics of graphene bombarded by fullerene. Acta Physica Sinica, 2014, 63(8): 083401. doi: 10.7498/aps.63.083401
[9]	Qin Wei-Yang, Sun Tao, Jiao Xu-Dong, Yang Yong-Feng. Chaos synchroniztion by function coupling in a class of nonlinear dynamical system. Acta Physica Sinica, 2012, 61(9): 090502. doi: 10.7498/aps.61.090502
[10]	Li Chun-Guang, Chen Jun. Circuit design of tabu learning neuron models and their dynamic behavior. Acta Physica Sinica, 2011, 60(2): 020502. doi: 10.7498/aps.60.020502
[11]	Li Li, Zhang Xin-Lu, Chen Li-Xue. Study on intrinsic optical bistability in Tm-doped laser crystal pumped at 648nm avalanche wavelength. Acta Physica Sinica, 2008, 57(1): 278-284. doi: 10.7498/aps.57.278
[12]	Li Jun, Dong Hai-Ying. Modelling of chaotic systems using wavelet kernel partial least squares regression method. Acta Physica Sinica, 2008, 57(8): 4756-4765. doi: 10.7498/aps.57.4756
[13]	Luo Yu-Feng, Zhong Cheng, Zhang Li, Yan Xue-Jian, Li Jin, Jiang Yi-Ming. An in situ method for characterizing the kinetics of the oxidation process of copper thin films via sheet resistance. Acta Physica Sinica, 2007, 56(11): 6722-6726. doi: 10.7498/aps.56.6722
[14]	Zhang Wei, Zhou Shu-Hua, Ren Yong, Shan Xiu-Ming. Bifurcation analysis and control in Turbo decoding algorithm. Acta Physica Sinica, 2006, 55(2): 622-627. doi: 10.7498/aps.55.622
[15]	Wang Long-Hai, Yu Jun, Wang Yun-Bo, Peng Gang, Liu Feng, Gao Jun-Xiong. A model of ferroelectric capacitors based on hysteresis loop. Acta Physica Sinica, 2005, 54(2): 949-954. doi: 10.7498/aps.54.949
[16]	Li Jian-Feng, Zhang Hong-Dong, Qiu Feng, Yang Yu-Liang. A new approach to study the dynamics of the deformation of vesicles discrete-space variational method. Acta Physica Sinica, 2005, 54(9): 4000-4005. doi: 10.7498/aps.54.4000
[17]	Fu Wen-Yu, Hou Xi-Miao, He Li-Xia, Zheng Zhi-Gang. Dynamics and statistics in few-body hard-ball systems. Acta Physica Sinica, 2005, 54(6): 2552-2556. doi: 10.7498/aps.54.2552
[18]	Ye Mei-Ying. Control of chaotic system based on least squares support vector machine modeling. Acta Physica Sinica, 2005, 54(1): 30-34. doi: 10.7498/aps.54.30
[19]	Meng Qing-Guo, Li Rui-Qu, Li Cun-Biao. A link between the turbulent cascade and the dynamics of transition. Acta Physica Sinica, 2004, 53(8): 2621-2624. doi: 10.7498/aps.53.2621
[20]	Wang Hong-Xia, He Chen. Dynamical behaviour of a cellular neural network. Acta Physica Sinica, 2003, 52(10): 2409-2414. doi: 10.7498/aps.52.2409

Catalog

Vol. 63, Issue 2 - 2014-01-20

Metrics

Abstract views: 5379
PDF Downloads: 691
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