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A meminductor is a new type of memory device. It is of importance to study meminductor model and its application in nonlinear circuit prospectively. For this purpose, we present a novel mathematical model of meminductor, which considers the effects of internal state variable and therefore will be more consistent with future actual meminductor device. By using several operational amplifiers, multipliers, capacitors and resistors, the equivalent circuit of the model is designed for exploring its characteristics. This equivalent circuit can be employed to design meminductor-based application circuits as a meminductor emulator. By employing simulation experiment, we investigate the characteristics of this meminductor driven by sinusoidal excitation. The characteristic curves of current-flux (i-φ), voltage-flux (v-φ), v-ρ (internal variable of meminductor) and φ-ρ for the meminductor model are given by theoretical analyses and simulations. The curve of current-flux (i-φ) is a pinched hysteretic loop passing through the origin. The area bounding each sub-loop deforms as the frequency varies, and with the increase of frequency, the shape of the pinched hysteretic loop tends to be a straight line, indicating a dependence on frequency for the meminductor. Based on the meminductor model, a meminductive Wien-bridge chaotic oscillator is designed and analyzed. Some dynamical properties, including equilibrium points and the stability, bifurcation and Lyapunov exponent of the oscillator, are investigated in detail by theoretical analyses and simulations. By utilizing Lyapunov spectrum, bifurcation diagram and dynamical map, it is found that the system has periodic, quasi-periodic and chaotic states. Furthermore, there exist some complicated nonlinear phenomena for the system, such as constant Lyapunov exponent spectrum and nonlinear amplitude modulation of chaotic signals. Moreover, we also find the nonlinear phenomena of coexisting bifurcation and coexisting attractors, including coexistence of two different chaotic attractors and coexistence of two different periodic attractors. The phenomenon shows that the state of this oscilator is highly sensitive to its initial valuse, not only for chaotic state but also for periodic state, which is called coexistent oscillation in this paper. The basic mechanism and potential applications of the existing attractors are illustrated, which can be used to generate robust pseudo random sequence, or multiplexed pseudo random sequence. Finally, by using the equivalent circuit of the proposed meminducive model, we realize an analog electronic circuit of the meminductive Wien-bridge chaotic system. The results of circuit experiment are displayed by the oscilloscope, which can verify the chaotic characteristics of the oscillator. The oscillator, as a pseudo random signal source, can be used to generate chaotic signals for the applications in chaotic cryptography and secret communications.
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Keywords:
- meminductor /
- Wien bridge /
- chaos /
- coexisting attractor
[1] Chua L O 1971 IEEE Trans. Circuit Theory 18 507
[2] Tour J M, He T 2008 Nature 453 42
[3] Strukov D B, Snider G S, Stewart D R, Williams R S 2008 Nature 453 80
[4] Mostafa H, Ismail Y 2016 IEEE Trans. Semicond. Manuf. 29 145
[5] Bass O, Fish A, Naveh D 2015 Radioengineering 24 425
[6] Duan S K, Hu X F, Dong Z K, Wang L D, Mazumder P 2015 IEEE Trans. Neural Networks Learn. Syst. 26 1202
[7] Wang L D, Duan M T, Duan S K, Hu X F 2014 Sci. China:Inform. Sci. 44 920(in Chinese)[王丽丹, 段美涛, 段书凯, 胡小方2014中国科学:信息科学44920]
[8] Semary M S, Malek H L A, Hassan H N, Radwan A G 2016 Microelectron. J. 51 58
[9] Yang X, Adeyemo A A, Jabir A, Mathew J 2016 Electron. Lett. 52 906
[10] Di Ventra M, Pershin Y V, Chua L O 2009 Proc. IEEE 97 1717
[11] Chua L O 1978 Guest Lectures of the 1978 European Conference on Circuit Theory and Design p81
[12] Chua L O 2003 Proc. IEEE 91 1830
[13] Chua L O 20092014 ACS Nano 8 10043
[14] Pershin Y V, Di Ventra M 2010 Electron. Lett. 46 517
[15] Pershin Y V, Di Ventra M 2011 Electron. Lett. 47 243
[16] Liang Y, Yu D S, Chen H 2013 Acta Phys. Sin. 62 158501 (in Chinese)[梁燕, 于东升, 陈昊2013 62 158501]
[17] Sah M P, Budhathoki R K, Yang C, Kim H 2014 Circ. Syst. Signal Pr. 33 2363
[18] Liang Y, Chen H, Yu D S 2014 IEEE Trans. Circuits Syst. Ⅱ 61 299
[19] Biolek D, Biolek Z, Biolková V 2011 Analog Integr. Circ. S. 66 129
[20] Wang H, Wang X, Li C D, Chen L 2013 Abstr. Appl. Anal. 2013 281675
[21] Zheng C Y, Yu D S, Liang Y, Chen M K 2015 Chin. Phys. B 24 110701
[22] Yuan F, Wang G Y, Jin P P 2015 Acta Phys. Sin. 64 210504 (in Chinese)[袁方, 王光义, 靳培培2015 64 210504]
[23] Wang G Y, Jin P P, Wang X W, Shen Y R, Yuan F, Wang X Y 2016 Chin. Phys. B 25 090502
[24] Yu Q, Bao B C, Xu Q, Chen M, Hu W 2015 Acta Phys. Sin. 64 170503 (in Chinese)[俞清, 包伯成, 徐权, 陈墨, 胡文2015 64 170503]
[25] Li Z J, Zeng Y C 2014 J. Electron. Inform. Technol. 36 88 (in Chinese)[李志军, 曾以成2014电子与信息学报3688]
[26] Yu J T, Li Y, Mu X M, Zhang J J, Miao X S, Wang S N 2015 Radioengineering 24 808
[27] Xu Z T, Jin K J, Gu L, Jin Y L, Ge C, Wang C, Guo H Z, Lu H B, Zhao R Q, Yang G Z 2012 Small 8 1279
[28] Shevchenko S N, van der Ploeg S H W, Grajcar M, Il'ichev E, Omelyanchouk A N, Meyer H G 2008 Phys. Rev. B 78 174527
[29] Chen M, Yu J J, Yu Q, Li C D, Bao B C 2014 Entropy 16 6464
[30] Deng W, Fang J, Wu Z J 2015 Optik 126 5468
[31] Li C B, Wang J, Hu W 2012 Nonlinear Dyn. 68 575
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[1] Chua L O 1971 IEEE Trans. Circuit Theory 18 507
[2] Tour J M, He T 2008 Nature 453 42
[3] Strukov D B, Snider G S, Stewart D R, Williams R S 2008 Nature 453 80
[4] Mostafa H, Ismail Y 2016 IEEE Trans. Semicond. Manuf. 29 145
[5] Bass O, Fish A, Naveh D 2015 Radioengineering 24 425
[6] Duan S K, Hu X F, Dong Z K, Wang L D, Mazumder P 2015 IEEE Trans. Neural Networks Learn. Syst. 26 1202
[7] Wang L D, Duan M T, Duan S K, Hu X F 2014 Sci. China:Inform. Sci. 44 920(in Chinese)[王丽丹, 段美涛, 段书凯, 胡小方2014中国科学:信息科学44920]
[8] Semary M S, Malek H L A, Hassan H N, Radwan A G 2016 Microelectron. J. 51 58
[9] Yang X, Adeyemo A A, Jabir A, Mathew J 2016 Electron. Lett. 52 906
[10] Di Ventra M, Pershin Y V, Chua L O 2009 Proc. IEEE 97 1717
[11] Chua L O 1978 Guest Lectures of the 1978 European Conference on Circuit Theory and Design p81
[12] Chua L O 2003 Proc. IEEE 91 1830
[13] Chua L O 20092014 ACS Nano 8 10043
[14] Pershin Y V, Di Ventra M 2010 Electron. Lett. 46 517
[15] Pershin Y V, Di Ventra M 2011 Electron. Lett. 47 243
[16] Liang Y, Yu D S, Chen H 2013 Acta Phys. Sin. 62 158501 (in Chinese)[梁燕, 于东升, 陈昊2013 62 158501]
[17] Sah M P, Budhathoki R K, Yang C, Kim H 2014 Circ. Syst. Signal Pr. 33 2363
[18] Liang Y, Chen H, Yu D S 2014 IEEE Trans. Circuits Syst. Ⅱ 61 299
[19] Biolek D, Biolek Z, Biolková V 2011 Analog Integr. Circ. S. 66 129
[20] Wang H, Wang X, Li C D, Chen L 2013 Abstr. Appl. Anal. 2013 281675
[21] Zheng C Y, Yu D S, Liang Y, Chen M K 2015 Chin. Phys. B 24 110701
[22] Yuan F, Wang G Y, Jin P P 2015 Acta Phys. Sin. 64 210504 (in Chinese)[袁方, 王光义, 靳培培2015 64 210504]
[23] Wang G Y, Jin P P, Wang X W, Shen Y R, Yuan F, Wang X Y 2016 Chin. Phys. B 25 090502
[24] Yu Q, Bao B C, Xu Q, Chen M, Hu W 2015 Acta Phys. Sin. 64 170503 (in Chinese)[俞清, 包伯成, 徐权, 陈墨, 胡文2015 64 170503]
[25] Li Z J, Zeng Y C 2014 J. Electron. Inform. Technol. 36 88 (in Chinese)[李志军, 曾以成2014电子与信息学报3688]
[26] Yu J T, Li Y, Mu X M, Zhang J J, Miao X S, Wang S N 2015 Radioengineering 24 808
[27] Xu Z T, Jin K J, Gu L, Jin Y L, Ge C, Wang C, Guo H Z, Lu H B, Zhao R Q, Yang G Z 2012 Small 8 1279
[28] Shevchenko S N, van der Ploeg S H W, Grajcar M, Il'ichev E, Omelyanchouk A N, Meyer H G 2008 Phys. Rev. B 78 174527
[29] Chen M, Yu J J, Yu Q, Li C D, Bao B C 2014 Entropy 16 6464
[30] Deng W, Fang J, Wu Z J 2015 Optik 126 5468
[31] Li C B, Wang J, Hu W 2012 Nonlinear Dyn. 68 575
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