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Chin. Phys. B, 2021, Vol. 30(12): 120502    DOI: 10.1088/1674-1056/abfa03
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Heterogeneous dual memristive circuit: Multistability, symmetry, and FPGA implementation

Yi-Zi Cheng(承亦梓), Fu-Hong Min(闵富红), Zhi Rui(芮智), and Lei Zhang(张雷)
School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing 210023, China
Abstract  An improved heterogeneous dual memristive circuit (DMC) is proposed based on Chua's circuit, which shows good symmetry and multistablility. For the difficulty in controlling the initial conditions, which restricts the engineering applications, the 3rd-order model (3OM) in flux-charge domain is derived from the 5th-order model (5OM) in volt-ampere domain by using the flux-charge analysis method (FCAM). The consistence of symmetry and multistability before and after dimensionality decreasing is meticulously investigated via bifurcation diagram, Lyapunov exponents, and especially attraction basins. The comparative analysis validates the effectiveness of reduction model and improves the controllability of the circuit. To avoid the noise in the analog circuit, a field-programmable gate array (FPGA) is utilized to realize the reduction model, which is rarely reported and valuable for relevant research and application.
Keywords:  memristive circuit      chaos      multistability      FPGA implementation  
Received:  23 March 2021      Revised:  06 April 2021      Accepted manuscript online:  21 April 2021
PACS:  05.45.-a (Nonlinear dynamics and chaos)  
  05.45.Pq (Numerical simulations of chaotic systems)  
  05.45.Gg (Control of chaos, applications of chaos)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 61971228 and 61871230), the Natural Science Foundations of Jiangsu Higher Education Institutions, China (Grant No. 19KJB520042), and the Postgraduate Research & Practice Innovation Program of Jiangsu Province, China (Grant No. SJCX21_0564).
Corresponding Authors:  Fu-Hong Min     E-mail:

Cite this article: 

Yi-Zi Cheng(承亦梓), Fu-Hong Min(闵富红), Zhi Rui(芮智), and Lei Zhang(张雷) Heterogeneous dual memristive circuit: Multistability, symmetry, and FPGA implementation 2021 Chin. Phys. B 30 120502

[1] Chua L O 1971 IEEE Trans. Circ. Theory 18 507
[2] Xin Y M, Li Y X, Huang X and Cheng Z S 2019 IEEE Trans. Cybern. 49 712
[3] Li C, Min F H and Li C B 2018 Nonlinear Dyn. 94 2785
[4] Yuan M M, Wang W P, Wang Z, Luo X and Kurths J 2021 IEEE Trans. Neural Netw. Lear. Syst. 32 151
[5] Bodo B, Armand Eyebe Fouda J S, Mvogo A and Tagne S 2018 Chaos, Solitons and Fractals 115 190
[6] Chang H, Li Y X, Chen G R and Yuan F 2020 Int. J. Bifurc. Chaos 30 2030019
[7] Peng Y X, Sun K H and He S B 2020 Chaos, Solitons and Fractals 137 109873
[8] Guo M, Zhang M, Dou M L, Dou G and Li Y X 2020 Chin. Phys. B 29 110505
[9] Chang H, Li Y and Chen G R 2019 Int. J. Bifurc. Chaos 29 1950086
[10] Guo M, Yang W Y, Xue Y B, Gao Z H, Yuan F and Dou G and Li Y X 2019 Chaos 29 043114
[11] Sun J W, Han G Y and Zeng Z G 2020 IEEE Trans. Cybern. 50 2935
[12] Li H, Sheng Y J, Yang S P, Peng M F and Han Y J 2021 Acta Phys. Sin. 70 040502 (in Chinese)
[13] Dong Y J, Wang G Y, Iu H H C, Chen G R and Chen L 2020 Chaos 30 103123
[14] Leonov G A, Kuznetsov N V and Modaev T N 2015 Commun. Nonlinear Sci. Numer. Simul. 28 166
[15] Chen J J, Yan D W, Duan S K and Wang L D 2020 Chin. Phys. B 29 110504
[16] Kengne J, Nguomkam Negou A and Tchiotsop D 2017 Nonlinear Dyn. 88 2589
[17] Li H M, Yang Y F, Li W, He S B and Li C L 2020 Eur. Phys. J. Plus 135 579
[18] Wang G Y, Yuan F, Chen G R and Zhang Y 2018 Chaos 28 013125
[19] Wang M J, Deng Y, Liao X H, Li Z J, Ma M L and Zeng Y C 2019 Int. J. Nonlinear Mech. 111 149
[20] Yang Y, Ren K C, Qian H and Yao X Y 2019 Eur. Phys. J. Spec. Top. 228 2011
[21] Lu Y M and Min F H 2019 Acta Phys. Sin. 68 130502 (in Chinese)
[22] Chen M, Feng Y, Bao H, Bao B C, Yu Y J, Wu H G and Xu Q 2018 Chaos Solitons Fract. 115 313
[23] Chen M, Sun M X, Bao H, Hu Y H and Bao B C 2020 IEEE Trans. Ind. Electron. 67 2197
[24] Corinto F and Forti M 2016 IEEE Trans. Circ. Syst. I:Reg. Paper 63 1997
[25] Zhang Y M, Guo M, Dou G, Li Y X and Chen G R 2018 Chaos 28 083121
[26] Peng G Y and Min F H 2017 Nonlinear Dyn. 90 1607
[27] Ruan J Y, Sun K H and Mou J 2016 Acta Phys. Sin. 65 190502 (in Chinese)
[28] Dong E Z, Li R H and Du S Z 2021 Chin. Phys. B 30 020505
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