Research of coupling behavior based on series-parallel flux-controlled memristor

Wang Yan; Yang Jiu; Wang Li-Dan; Duan Shu-Kai

doi:10.7498/aps.64.237303

Abstract

Memristor is a nanoscale element with low power consumption and high integration, having great potential in applications. A single memristor has rich electrical properties, and its series-parallel circuit exhibits more abundant dynamic behaviors. However, memristors' coupled effects cannot be ignored in high-density integrated environment. Therefore, this paper first deduces the mathematical model of coupled memristor in detail based on the coupled flux controlled memristors. Second, considering the different polarity connection and coupling strength, we discuss the coupled condition of two flux-controlled memristors in series and parallel connections. Then the detailed theoretical analysis is illustrated, and the variation of memristance in terms of voltage, time and flux as well as the relations between voltage and currents are examined via numerical simulations to further explore the influence of coupled effects on the memristive system. At the same time, a graphical user interface of series-parallel coupled circuit based on Matlab is designed. Through this interface, we can adjust the initial value of memristor and coupling coefficient, select different connection modes, obtain corresponding connection diagram and output waveform which intuitively show the dynamic behavior of different parameters directly and provide experimental reference for further study of the circuit design. Furthermore, this paper shows the influence of initial value on the normal working range of memristors in the presence of coupling. From the table 1 it can be easily obtained that when the memristors are connected in the same direction, the range of memristance without coupling is greater than that with coupling. And the situation is opposite when the memristors are connected in different directions. Finally, the hysteresis curve with different coupling coefficients and the change of memristance with time are shown via building the Pspice simulator of coupled memristors, so the coupling effects of memristor is confirmed by circuit simulations. Experimental results reflect that the coupling with the same polarity enhances the change of resistance, and the coupling with different polarity with slow down it. Such dynamical properties can be well utilized in memristive networks and provide a strong theoretical basis for the comprehensive consideration of the design of memristive system.

Keywords:

Authors and contacts

1.
School of Electronic and Information Engineering, Southwest University, Chongqing 400715, China

Corresponding author: Wang Li-Dan, ldwang@swu.edu.cn

Funds: Project supported by the Program for New Century Excellent Talents in University of Ministry of Education of China (Grant No. [2013]47), the National Natural Science Foundation of China (Grant Nos. 61372139, 61571372, 60972155), the Spring Sunshine Plan Research Project of Ministry of Education of China (Grant No. z2011148), the Technology Foundation for Selected Overseas Chinese Scholars, Ministry of Personnel in China (Grant No. [2012]186), the University Excellent Talents Supporting Foundation of Chongqing, China (Grant No. [2011]65), the University Key Teacher Supporting Foundation of Chongqing, China (Grant No. [2011]65), and the Fundamental Research Fund for the Central Universities, China (Grant Nos. XDJK2014A009, XDJK2013B011).

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Cited By

[1]	Chua L O 1971 IEEE Trans. Circ. Syst.I. 18 507
[2]	Williams R S 2008 IEEE Spectr. 45 28
[3]	Strukov D B, Snider G S, Stewart D R, Williams R S 2008 Nature 453 80
[4]	Biolek Z, Biolek D, Biolkova V 2009 Radio. Eng 18 210
[5]	Adhikari S P, Sah M P, Kim H, Chua L O 2013 IEEE Trans. Circ. Syst.I. 60 3008
[6]	Ho Y, Huang G M, Li P 2011 IEEE Trans. Circ. Syst.I. 58 724
[7]	Hu X F, Duan S K, Wang L D, Liao X F 2012 Sci. China Inf. Sci. 55 461
[8]	Duan S K, Hu X F Wang L D, Li C D, Mazumder P 2012 Sci. China Inf. Sci. 55 1446
[9]	Zhou J, Huang D 2012 Chin. Phys. B 21 048401
[10]	Bao B C, Hu F W, Liu Z, Xu J P 2014 Chin. Phys. B 23 070503
[11]	Chua L 2011 Appl. Phy. A 102 765
[12]	Jo S H, Chang T, Ebong I, Bhadviya B B, Mazumder P, Lu W 2010 Nano Lett 10 1297
[13]	Shin S, Kim K, Kang S M 2013 IEEE Trans. Circ. Syst.I. 60 1241
[14]	Wang X B, Chen Y R, Xi H W, Li H 2009 IEEE Elec. Dev. Lett. 30 294
[15]	Kvatinsky S, Friedman E G, Kolodny A, Weiser U C 2013 IEEE Trans. Circ. Syst.I. 60 211
[16]	Wang L D, Drakakis E, Duan S K, He P F 2012 Int. J. Bifurcat. Chaos 22 1250205
[17]	Budhathoki R K, Sah M P, Adhikari S P, Kim H, Chua L O 2013 IEEE Trans. Circ. Syst.I. 60 2688
[18]	Yin W H, Wang L D, Duan S K 2013 Appl. Mech. Mater. 284 2485
[19]	Dong Z K, Duan S K, Hu X F, Wang L D 2014 Acta Phys.Sin. 63 128502 (in Chinese)[董哲康, 段书凯, 胡小方, 王丽丹 2014 物理学报 63 128502]
[20]	Budhathoki R K, Sah M P D, Yang C, Kim H, Chua L O 2014 Int. J. Bifurcat. Chaos 24 1430006
[21]	Cai W R, Tetzlaff R 2014 2014 IEEE International Symposium on Circuits and Systems (ISCAS) Melbourne VIC, June 1259-1262, 2014
[22]	Yu D S, Iu H H C, Liang Y, Fernando T, Chua L O 2015 IEEE Trans. Circ. Syst.I. 62 1607

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

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