中国物理B ›› 2024, Vol. 33 ›› Issue (3): 30505-030505.doi: 10.1088/1674-1056/acf281

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Coexistence behavior of asymmetric attractors in hyperbolic-type memristive Hopfield neural network and its application in image encryption

Xiaoxia Li(李晓霞)1,2,†, Qianqian He(何倩倩)1,2,3, Tianyi Yu(余天意)1,2, Zhuang Cai(才壮)1,2, and Guizhi Xu(徐桂芝)1,2   

  1. 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
  • 收稿日期:2023-06-20 修回日期:2023-08-16 接受日期:2023-08-22 出版日期:2024-02-22 发布日期:2024-02-29
  • 通讯作者: Xiaoxia Li E-mail:lixiaoxia@hebut.edu.cn
  • 基金资助:
    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).

Coexistence behavior of asymmetric attractors in hyperbolic-type memristive Hopfield neural network and its application in image encryption

Xiaoxia Li(李晓霞)1,2,†, Qianqian He(何倩倩)1,2,3, Tianyi Yu(余天意)1,2, Zhuang Cai(才壮)1,2, and Guizhi Xu(徐桂芝)1,2   

  1. 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
  • Received:2023-06-20 Revised:2023-08-16 Accepted:2023-08-22 Online:2024-02-22 Published:2024-02-29
  • Contact: Xiaoxia Li E-mail:lixiaoxia@hebut.edu.cn
  • Supported by:
    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).

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摘要： 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.

关键词: hyperbolic-type memristor, Hopfield neural network (HNN), asymmetric attractors, image encryption

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.

Key words: hyperbolic-type memristor, Hopfield neural network (HNN), asymmetric attractors, image encryption

中图分类号:  (Nonlinear dynamics and chaos)

  • 05.45.-a