A fractional-order memristor model and the fingerprint of the simple series circuits including a fractional-order memristor

Yu Ya-Juan; Wang Zai-Hua

doi:10.7498/aps.64.238401

Abstract

A memristor is a nonlinear resistor with time memory. The resistance of a classical memristor at a given time is represented by the integration of all the full states before the time instant, a case of ideal memory without any loss. Recent studies show that there is a memory loss of the HP TiO2 linear model, in which the width of the doped layer of HP TiO2 model cannot be equal to zero or the whole width of the model. Based on this observation, a fractional-order HP TiO2 memristor model with the order between 0 and 1 is proposed, and the fingerprint analysis of the new fractional-order model under periodic external excitation is made, thus the formula for calculating the area of hysteresis loop is obtained. It is found that the shape and the area enclosed by the hysteresis loop depend on the order of the fractional-order derivative. Especially, for exciting frequency being bigger than 1, the memory strength of the memristor takes its maximal value when the order is a fractional number, not an integer. Then, the current-voltage characteristics of the simple series one-port circuit composed of the fractional-order memristor and the capacitor, or composed of the fractional-order memristor and the inductor are studied separately. Results demonstrate that at the periodic excitation, the memristor in the series circuits will have capacitive properties or inductive properties as the fractional order changes.

Keywords:

Authors and contacts

Yu Ya-Juan^1,2,
Wang Zai-Hua^1,3

1.
State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China;
2.
School of Mathematics and Physics，Changzhou University, Changzhou 213164, China;
3.
Institute of Science，PLA University of Science and Technology, Nanjing 211101, China

Corresponding author: Wang Zai-Hua, zhwang@nuaa.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11372354).

References

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[3]	Strukov D B, Snider G S, Stewart D R, Williams R S 2008 Nature 453 80
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[14]	Yuan F, Wang G Y, Wang X Y 2015 Chin. Phys. B 24 060506
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[22]	Hilfer R 2000 Applications of fractional calculus in physics (Singapore: World Scientific Publishing Co Pte Ltd) 430
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[27]	Monje C A, Chen Y Q, Vinagre B M, Xue D Y, Feliu V 2010 Fractional-order Systems and Controls: Fundamentals and Applications(London: Springer-Verlag)
[28]	Podlubny I 1999 Fractional Differential Equations (SanDiego: Academic Press)
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Cited By

[1]	Chua L O 1971 IEEE Trans. Circ. Theory 18 507
[2]	Chua L O, Kang S M 1976 Proc IEEE 64 209
[3]	Strukov D B, Snider G S, Stewart D R, Williams R S 2008 Nature 453 80
[4]	Williams R S 2008 IEEE Spectrum 45 24
[5]	Pershin Y V, Di Ventra M 2008 Phys. Rev. B 78 113309
[6]	Wang X B, Chen Y R, Xi H, Li H, Dimitrov D 2009 IEEE Electron Device Letters 30 294
[7]	Borghetti J, Li Z, Straznicky J, Li X, Ohlberg D A, Wu W, Stewart D R, Williams R S 2009 Proc Natl Acad Sci. USA 106 1699
[8]	Borghetti J, Snider G S, Kuekes P J, Yang J J, Stewart D R, Williams R S 2010 Nature 464 873
[9]	Thomas A 2013 J. Phys. D: Appl. Phys. 46 093001
[10]	Hu X F, Duan S K, Wang L D, Liao X F 2011 Sci. China: Informationis 41 500 (in Chinese) [胡小方, 段书凯, 王丽丹, 廖晓峰 2011 中国科学: 41 500]
[11]	Cai K P, Wang R, Zhou J 2010 Electronic Components and Materials 29 78 (in Chinese) [蔡坤鹏, 王睿, 周济 2010 电子元件与材料 29 78]
[12]	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]
[13]	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]
[14]	Yuan F, Wang G Y, Wang X Y 2015 Chin. Phys. B 24 060506
[15]	Strukov D B, Williams R S 2009 Appl. Phys. A 94 515
[16]	Shkabko A, Aguirre M H, Marozau I, Lippert T, Weidenkaff A 2009 Appl. Phys. Lett. 95 152109
[17]	Muthuswamy B, Chua L O 2010 Int. J. Bifurcation and Chaos 20 1567
[18]	Adhikari S P, Sah M P, Kim H, Chua L O 2013 IEEE Trans. Circ. Syst. I: Regular Papers 60 3008
[19]	Kim H, Sah M P, Yang C J, Seongik C, Chua L O 2012 IEEE Trans. Circ. Syst. I: Regular Papers 59 2422
[20]	Corinto F, Ascoli A 2012 IEEE Trans. Circuits Syst. I: Regular Papers 59 2713
[21]	Xu M Y, Tan W C 2002 Sci. China Ser. A 32 673 (in Chinese) [徐明瑜, 谭文长 2002 中国科学 A辑 32 673]
[22]	Hilfer R 2000 Applications of fractional calculus in physics (Singapore: World Scientific Publishing Co Pte Ltd) 430
[23]	Fouda M E, Radwan A G 2013 J. Frac. Calcu. Appl. 4 1
[24]	Cafagna D, Grassi G 2012 Nonlinear Dyn. 70 1185
[25]	Sabatier J, Agrawal O P, Machado J A 2007 Advances in Fractional Calculus (Netherlands: Springer) 419
[26]	Podlubny I 1999 IEEE Trans. Autom. Control 44 208
[27]	Monje C A, Chen Y Q, Vinagre B M, Xue D Y, Feliu V 2010 Fractional-order Systems and Controls: Fundamentals and Applications(London: Springer-Verlag)
[28]	Podlubny I 1999 Fractional Differential Equations (SanDiego: Academic Press)
[29]	Rossikhin Yu A, Shitikova M V 2010 Applied Mechanics Reviews 63 010801
[30]	Wang Z H, Hu H Y 2009 Sci. China Ser. G 39 1495 (in Chinese) [王在华, 胡海岩 2009 中国科学 G 辑 39 1495]
[31]	Biolek D, Biolek Z, Biolková V 2014 Electron Lett. 50 74
[32]	Biolek Z, Biolek D, Biolková V 2012 IEEE Trans. Circ. Syst. II: Exp.Briefs 59 607

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Vol. 64, Issue 23 - 2015-12-05

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