Abstract
Hopfield neural network is an import cornerstone of neural network research. The dynamic analysis has always been a hot topic of the Hopfield neural network research. Memristor, the fourth-generation electronic device, is considered to be ideal nonlinear device applied in neural networks. In this work, we propose a novel time-delay locally active memristor, which has abundant dynamical behaviors. Characteristics of the proposed memristor are analyzed by power-off plot, DC V–I plot and pinched hysteresis loops plot. We applied the novel time-delay locally active memristor to a Hopfield neural to investigate the dynamic of the network. It is interesting that the proposed neural network has abundant dynamic behaviors, such as coexisting attractors, chaotic attractors and hyperchaotic attractors. The interesting phenomena are illustrated through bifurcation diagram, Lyapunov exponents diagram, and phase portraits. The electrical circuit of the proposed memristor and the Hopfield neural network is designed and simulated. The circuit simulation results are well consistent with the numerical simulation. Moreover, we propose an application of the Hopfield neural network to chaotic image encryption. Histogram, correlation, information entropy, and key sensitivity show that the simple image encryption scheme has high security and reliable encryption performance.
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L.O. Chua, IEEE Trans. Circuit Syst. 18, 507 (1971)
D.B. Strukov, G.S. Sinder, D.R. Stewart, R.S. Williams, Nature 453, 80 (2008)
B.C. Bao, Z.H. Ma, J.P. Xu, Z. Liu, Q. Xu, Int. J. Bifurcat. Chaos 21, 2629 (2011)
M. Bharathwaj, Int. J. Bifurcat. Chaos 20, 1335 (2010)
T. Lin, H.H.C. Lu, X.Y. Wang, X.K. Wang, Nonlinear Dyn. 77, 231–241 (2014)
T. Andy, J. Phys. D Appl. Phys. 46, 093001 (2013)
P. Yao, H.Q. Wu, B. Guo, J.S. Tang, Q.T. Zhang, W.Q. Zhang, J.J. Yang, H. Qian, Nature 577, 641 (2020)
S. Daniel, D.C. Sotan, G. Asaf, K. Avinoam, K. Shahar, IEEE Trans. Neural Netw. Learn. Syst. 26, 2408 (2015)
S.P. Wen, X.D. Xie, Y. Zhang, T.W. Huang, Z.G. Zeng, Neural Netw. 103, 142 (2018)
Y. Ho, G.M. Huang, P. Li, Nonvolatile memristor memory: device characteristics and design implications. Proceedings of the 2009 International Conference on Computer-Aided Design, San Jose, California, ICCAD ’09 (Association for Computing Machinery, New York, 2009), pp. 485–490. https://doi.org/10.1145/1687399.1687491
X. Zhu, X.J. Yang, C.Q. Wu, N. Xiao, J.J. Wu, X. Yi, IEEE Trans. Circuits Syst. II Express Briefs 60, 682 (2013)
Z.A. Mohammed, A.H.F. Hossam, M.H. Muhammad, N.S. Khaled, Microelectron. J. 44, 176 (2013)
J.J. Hopfield, Proc. Natl. Acad. Sci. 81, 3088 (1984)
G. Pajares, IEEE Trans. Neural Networks 17, 1250 (2006)
M. Liu, F.R. Yu, Y. Teng, V.C.M. Leung, M. Song, IEEE Trans. Veh. Technol. 67, 11008 (2018)
X.Y. Wang, Z.M. Li, Opt. Lasers Eng. 115, 107 (2019)
A. Babloyantz, C. Lourenco, Int. J. Neural Syst. 7, 461 (1996)
Ł Laskowski, Neural Comput. Appl. 23, 2435 (2013)
Y. Li, J. Li, J. Li, S.K. Duan, L.D. Wang, M.J. Guo, Neurocomputing 454, 382 (2021)
B. Bao, H. Qian, Q. Xu, M. Chen, J. Wang, Y.J. Yu, Front. Comput. Neurosci. 11, 81 (2017)
Q. Xu, Z. Song, H. Bao, M. Chen, B.C. Bao, AEU-Int. J. Electron. Commun. 96(66), 66–74 (2018)
C. Chen, J. Chen, H. Bao, M. Chen, B.C. Bao, Nonlinear Dyn. 95, 3385 (2019)
Z.T. Njitacke, J. Kengne, H.B. Fotsin, Int. J. Dyn. Control 7, 36 (2019)
H. Lin, C.H. Wang, Y. Tan, Nonlinear Dyn. 99, 2369 (2020)
Y. Leng, D. Yu, Y. Hu, Chaos: Interdisciplin. J. Nonlinear Sci. 30, 033108 (2020)
D. Mehdi, R. Salehi, Comput. Phys. Commun. 181, 1255 (2010)
K. Hina, S.J. Liao, R.N. Mohapatra, K. Vajravelu, Commun. Nonlinear Sci. Numer. Simul. 14, 3141 (2009)
C. Kunal, M. Chakraborty, T.K. Kar, Nonlinear Anal. Hybrid Syst 5, 613 (2011)
R.D.V. Ramana, A. Sen, G.L. Johnston, Phys. Rev. Lett. 80, 5109 (1998)
Y.T. Kamal, O. Ito, J. Dyan. Syst. Meas. Control 112, 133 (1990)
S.N.A.P.D.S. Evesque, A.M. Annaswamy, S. Niculescu, A.P. Dowling, J. Dyan. Syst. Meas. Control 125, 186 (2003)
D.P. Magee, Optimal arbitrary time-delay filtering to minimize vibration in elastic manipulator systems. ProQuest Dissertations and Theses, pp. 6524–6524 (1997). https://www.proquest.com/dissertations-theses/optimal-arbitrary-time-delay-filtering-minimize/docview/304288622/se-2?accountid=30627
A.K. Agrawal, J.N. Yang, Earthquake Eng. Struct. Dynam. 29, 37 (2000)
H.J. Gao, T.W. Chen, J. Lam, Automatica 44, 39 (2008)
F.Z. Wang, N. Helian, S. Wu, IEEE Electron Device Lett. 31, 755 (2010)
V.T. Pham, A. Buscarino, L. Fortuna, M. Frasca, Int. J. Bifurc. Chaos 23, 1350073 (2013)
W. Hu, D. Ding, Y. Zhang, N. Wang, D. Liang, Optik 130, 189 (2017)
R. Li, R. Ding, Int. J. Mod. Phys. B 35, 2150166 (2021)
L. Chua, Radioengineering 24, 319 (2015)
L.F. Shampine, S. Thompson, Appl. Numer. Math. 37(4), 44–458 (2001)
A. Maus, J.C. Sprott, Commun. Nonlinear Sci. Numer. Simulat. 16, 3294–3302 (2011)
Q. Xu, Z. Song, H. Bao, M. Chen, B. Bao, AEU-Int. J. Electron. Commun. 96, 66–74 (2018)
S. Zhang, C. Li, J. Zheng, X. Wang, Z. Zeng, G. Chen, IEEE Trans. Circuits Syst. I: Regular Papers 68(12), 4945–4956 (2021)
S. Zhang, C. Li, J. Zheng, X. Wang, Z. Zeng, X. Peng, IEEE Transactions on Industrial Electronics, https://doi.org/10.1109/TIE.2021.3099231
S. Zhang, J. Zheng, X. Wang, Z. Zeng, S. He, Nonlinear Dyn. 102(4), 2821–2841 (2020)
D. Biswas, T. Banerjee, Nonlinear Dyn. 83(4), 2331–2347 (2016)
B. Tanmoy, D. Biswas, B.C. Sarkar, Bonfring Int. J. Power Syst. Integrat. Circuits 2, 13 (2012)
B. Norouzi, S. Mirzakuchaki, Multimed. Tools Appl. 76, 13681 (2017)
G. Maddodi, A. Awad, D. Awad, Multimed. Tools Appl. 77, 24701 (2018)
C. Lakshmi, K. Thenmozhi, J. Rayappan, Neural Comput. Appl. 32, 11477 (2020)
H. Lin, C. Wang, F. Yu, IEEE Trans. Ind. Electron. 68, 12708 (2020)
C. Lakshimi, K. Thenmozhi, J.B.B. Rayappan, R. Amirtharajan, Neural Comput. Appl. 32, 11477–11489 (2020)
S. Zhang, J. Zheng, X. Wang, Z. Zeng, Chaos 31, 011101 (2021)
H. Bao, Z. Hua, W. Liu, B. Bao, Sci. China Technol. Sci 64, 2281–2291 (2021)
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This work was supported by the Key Scientific and Technological Project in Henan Province (182102210508).
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Li, R., Ding, R. A novel locally active time-delay memristive Hopfield neural network and its application. Eur. Phys. J. Spec. Top. 231, 3005–3017 (2022). https://doi.org/10.1140/epjs/s11734-022-00560-3
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DOI: https://doi.org/10.1140/epjs/s11734-022-00560-3