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Memristor with memory function is the fourth fundamental two-terminal circuit element, besides resistor, capacitor and inductor. In this paper, a smooth flux-controlled memristor is described by a monotone-increasing nonlinearity curve in the -q plane, and it has an italic type 8 like voltage current relation curve that looks like a pinched hysteresis loop characteristics. By replacing Chua's diode with an active memristor consisting of a smooth flux-controlled memristor and a negative conductance, a memristor based chaotic oscillation is derived from Chua's circuit. Furthermore, the equivalent circuit implementation form for the active memristor is designed by utilizing conventional components such as operational amplifiers and multipliers. The results from theoretical analysis, numerical simulations and circuit simulations are completely identical with each other, and demonstrate that the dynamical behaviors of the memristor chaotic circuit are dependent on the memristor initial state, showing different orbits such as chaotic oscillation, periodic oscillation and stable sink under different initial states.
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Keywords:
- memristor /
- chaotic circuit /
- initial state /
- equivalent circuit
[1] Chua L O 1971 IEEE Trans. Circuit Theory 18 507
[2] Chua L O, Kang S M 1976 Proc. IEEE 64 209
[3] [4] Strukov D B, Snider G S, Stewart D R, Williams R S 2008 Nature 453 80
[5] [6] [7] Tour J M, He T 2008 Nature 453 42
[8] [9] Wey T A, Benderli S 2009 Electron. Lett. 45 1103
[10] Witrisal K 2009 Electron. Lett. 45 713
[11] [12] [13] Biolek Z, Biolek D, Biolkov V 2009 Radioengineering 18 210
[14] [15] Joglekar Y N, Wolf S J 2009 Eur. J. Phys. 30 661
[16] Itoh M, Chua L O 2008 Int. J. Bifur. Chaos 18 3183
[17] [18] Muthuswamy B 2009 IETE Techn. Rev. 26 415
[19] [20] Bao B C, Liu Z, Xu J P 2010 Electron. Lett. 46 228
[21] [22] Bao B C, Liu Z, Xu J P 2010 Chin. Phys. B 19 030510
[23] [24] 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]
[25] [26] Barboza R, Chua L O 2008 Int. J. Bifur. Chaos 18 943
[27] [28] Bao B C, Li C B, Xu J P, Liu Z 2008 Chin. Phys. B 17 4022
[29] [30] Li C B, Wang D C 2009 Acta Phys. Sin. 58 764 (in Chinese) [李春彪、王德纯 2009 58 764]
[31] [32] [33] Wang X, Chen Y, Xi H, Dimitrov D 2009 IEEE Electron Device Lett. 30 294
[34] [35] Pershin Y V, Ventra M D 2008 Phys. Rev. B 78 113309
[36] [37] Zhong G 1994 IEEE Trans. Circuits Syst. 41 934
[38] [39] Muthuswamy B 2010 Int. J. Bifur. Chaos 20 1335
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[1] Chua L O 1971 IEEE Trans. Circuit Theory 18 507
[2] Chua L O, Kang S M 1976 Proc. IEEE 64 209
[3] [4] Strukov D B, Snider G S, Stewart D R, Williams R S 2008 Nature 453 80
[5] [6] [7] Tour J M, He T 2008 Nature 453 42
[8] [9] Wey T A, Benderli S 2009 Electron. Lett. 45 1103
[10] Witrisal K 2009 Electron. Lett. 45 713
[11] [12] [13] Biolek Z, Biolek D, Biolkov V 2009 Radioengineering 18 210
[14] [15] Joglekar Y N, Wolf S J 2009 Eur. J. Phys. 30 661
[16] Itoh M, Chua L O 2008 Int. J. Bifur. Chaos 18 3183
[17] [18] Muthuswamy B 2009 IETE Techn. Rev. 26 415
[19] [20] Bao B C, Liu Z, Xu J P 2010 Electron. Lett. 46 228
[21] [22] Bao B C, Liu Z, Xu J P 2010 Chin. Phys. B 19 030510
[23] [24] 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]
[25] [26] Barboza R, Chua L O 2008 Int. J. Bifur. Chaos 18 943
[27] [28] Bao B C, Li C B, Xu J P, Liu Z 2008 Chin. Phys. B 17 4022
[29] [30] Li C B, Wang D C 2009 Acta Phys. Sin. 58 764 (in Chinese) [李春彪、王德纯 2009 58 764]
[31] [32] [33] Wang X, Chen Y, Xi H, Dimitrov D 2009 IEEE Electron Device Lett. 30 294
[34] [35] Pershin Y V, Ventra M D 2008 Phys. Rev. B 78 113309
[36] [37] Zhong G 1994 IEEE Trans. Circuits Syst. 41 934
[38] [39] Muthuswamy B 2010 Int. J. Bifur. Chaos 20 1335
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