1 Key Laboratory of Electromagnetic Field and Electrical Apparatus Reliability of Hebei Province, Hebei University of Technology, Tianjin 300130, China; 2 State Key Laboratory of Reliability and Intelligence of Electrical Equipment, Hebei University of Technology, Tianjin 300130, China; 3 School of Life Science & Health Engineering, Hebei University of Technology, Tianjin 300130, China
Abstract The neuron model has been widely employed in neural-morphic computing systems and chaotic circuits. This study aims to develop a novel circuit simulation of a three-neuron Hopfield neural network (HNN) with coupled hyperbolic memristors through the modification of a single coupling connection weight. The bistable mode of the hyperbolic memristive HNN (mHNN), characterized by the coexistence of asymmetric chaos and periodic attractors, is effectively demonstrated through the utilization of conventional nonlinear analysis techniques. These techniques include bifurcation diagrams, two-parameter maximum Lyapunov exponent plots, local attractor basins, and phase trajectory diagrams. Moreover, an encryption technique for color images is devised by leveraging the mHNN model and asymmetric structural attractors. This method demonstrates significant benefits in correlation, information entropy, and resistance to differential attacks, providing strong evidence for its effectiveness in encryption. Additionally, an improved modular circuit design method is employed to create the analog equivalent circuit of the memristive HNN. The correctness of the circuit design is confirmed through Multisim simulations, which align with numerical simulations conducted in Matlab.
Received: 20 June 2023
Revised: 16 August 2023
Accepted manuscript online: 22 August 2023
PACS:
05.45.-a
(Nonlinear dynamics and chaos)
Fund: Project supported by the National Nature Science Foundation of China (Grant Nos. 51737003 and 51977060) and the Natural Science Foundation of Hebei Province (Grant No. E2011202051).
Corresponding Authors:
Xiaoxia Li
E-mail: lixiaoxia@hebut.edu.cn
Cite this article:
Xiaoxia Li(李晓霞), Qianqian He(何倩倩), Tianyi Yu(余天意),Zhuang Cai(才壮), and Guizhi Xu(徐桂芝) Coexistence behavior of asymmetric attractors in hyperbolic-type memristive Hopfield neural network and its application in image encryption 2024 Chin. Phys. B 33 030505
[1] Xu Q, Chen X and Chen B 2023 Nonlinear Dyn.111 8737 [2] Ma J 2023 Journal of Zhejiang University-SCIENCE A24 109 [3] Müller E J, Munn B R and Shine J M 2020 Nat. Commun.11 6337 [4] Ma J and Tang J 2017 Nonlinear Dyn.89 1569 [5] Hu T, Zhang J and Wang J 2023 Journal of Medicinal Chemistry66 4434 [6] Fusar-Poli P, de Pablo G S and Correll C U 2020 JAMA Psychiatry77 755 [7] Dai Z, Lin Q and Li T 2019 Neurobiology of Aging75 71 [8] Wen Z, Wang C and Deng Q 2022 Nonlinear Dyn.110 3823 [9] Li Z, Zhou H and Wang M 2021 Nonlinear Dyn.104 1455 [10] Chen M, Qi J W and Wu H G 2020 Science China Technological Sciences63 1035 [11] Yu Y, Shi M and Kang H 2020 Nonlinear Dyn.100 891 [12] Qi G, Wu Y and Hu J 2021 International Journal of Bifurcation and Chaos31 2150170 [13] Wouapi M K, Fotsin B H and Ngouonkadi E B M 2021 Cognitive Neurodynamics15 315 [14] Xu Q, Liu T and Feng C T 2021 Chin. Phys. B30 128702 [15] Hopfield J J 1984 Proc. Natl. Acad. Sci. USA81 3088 [16] Ding S, Wang N and Bao H 2023 Chaos, Solitons & Fractals166 112899 [17] Chen L, Yin H and Huang T 2020 Neural Networks125 174 [18] Doubla I S, Ramakrishnan B and Tabekoueng Z N 2022 Euro. Phys. J. Spec. Top.231 2371 [19] Wan Q, Li F and Chen S 2023 Chaos, Solitons & Fractals169 113259 [20] Hu Z and Wang C 2024 Multimedia Tools and Applications83 97 [21] Strukov D B, Snider G S and Stewart D R 2008 Nature453 80 [22] Zhang S, Zheng J and Wang X 2021 Chaos31 011101 [23] Chen C and Min F 2022 Euro. Phys. J. Plus137 841 [24] Leng Y, Yu D and Hu Y 2020 Chaos30 033108 [25] Ding D, Xiao H and Yang Z 2022 Nonlinear Dyn.108 4433 [26] Mondal A, Upadhyay R K and Ma J 2019 Cognitive Neurodynamics13 393 [27] Qiao S and An X L 2021 Pramana95 72 [28] Ma J, Zhang G and Hayat T 2019 Nonlinear Dyn.95 1585 [29] Li J, Liu S and Liu W 2016 Nonlinear Dyn.83 801 [30] Lin H, Wang C, Yu F, Hong Q, Xu C and Sun Y 2023 IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems42 4948 [31] Lin H, Wang C and Yu F 2023 IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems [32] Ma T, Mou J and Yan H 2022 Euro. Phys. J. Plus137 1 [33] Parastesh F, Jafari S and Azarnoush H 2019 Euro. Phys. J. Spec. Top.228 2023 [34] Zhang S, Zheng J and Wang X 2020 Nonlinear Dyn.102 2821 [35] Yu F, Zhang Z and Shen H 2022 Chin. Phys. B31 020505 [36] Gong L H, Luo H X and Wu R Q 2022 Physica A591 126793 [37] Gong L H and Luo H X 2023 Optics & Laser Technology167 109665 [38] Zhou N R, Tong L J and Zou W P 2023 Signal Processing211 109107 [39] Su Y, Wang X and Lin S 2022 Chin. Phys. B31 110503 [40] Lai Q, Lai C and Zhang H 2022 Chaos Solitons Fractals158 112017 [41] Liu L, Zhang L and Jiang D 2019 IEEE Access7 185796 [42] Tlelo-Cuautle E, Díaz-Muñoz J D and González-Zapata 2020 Sensors20 1326 [43] Yu F, Kong X and Mokbel A A M 2022 IEEE Transactions on Circuits and Systems II Express Briefs70 326 [44] Njitacke Z T, Isaac S D and Nestor T 2021 Neural Comput. Appl.33 6733 [45] Yu F, Shen H, Yu Q, et al 2022 IEEE Transactions on Network Science and Engineering10 845 [46] Shen H, Yu F and Kong X 2022 Chaos32 083133 [47] Njitacke Z T, Kengne J and Fotsin H B 2019 International Journal of Dyn. and Control7 36 [48] Lin H, Wang C and Chen C 2021 IEEE Trans Circuits Syst. I68 3397 [49] Bao H, Hu A and Liu W 2019 IEEE transactions on neural networks and learning systems31 502 [50] Bao H, Chen Z G and Cai J M 2022 Science China Technological Sciences65 2582
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