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

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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 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 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 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 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 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 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 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 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

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

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