中国物理B ›› 2025, Vol. 34 ›› Issue (12): 120506-120506.doi: 10.1088/1674-1056/adfeff

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Multi-scroll hopfield neural network excited by memristive self-synapses and its application in image encryption

Ting He(何婷)1, Fei Yu(余飞)2, Yue Lin(林越)1, Shaoqi He(何邵祁)2, Wei Yao(姚卫)2, Shuo Cai(蔡烁)2, and Jie jin(金杰)3,†   

  1. 1 School of Computer Science and Technology, ChangSha University of Science and Technology, Changsha 410114, China;
    2 School of Physics and Electronic Science, ChangSha University of Science and Technology, Changsha 410114, China 3 School of Information Engineering, Changsha Medical University, Changsha 410219, China
  • 收稿日期:2025-08-06 修回日期:2025-08-20 接受日期:2025-08-26 发布日期:2025-12-10
  • 通讯作者: Jie jin E-mail:jj67123@hnust.edu.cn
  • 基金资助:
    This project was supported by the Guiding Science and Technology Plan Project of Changsha City under Grant kzd2501129, by the Natural Science Foundation of Hunan Province (Grant No. 2025JJ50368), the Scientific Research Fund of Hunan Provincial Education Department (Grant No. 24A0248), and the National Natural Science Foundation of China (Grant No. 62273141).

Multi-scroll hopfield neural network excited by memristive self-synapses and its application in image encryption

Ting He(何婷)1, Fei Yu(余飞)2, Yue Lin(林越)1, Shaoqi He(何邵祁)2, Wei Yao(姚卫)2, Shuo Cai(蔡烁)2, and Jie jin(金杰)3,†   

  1. 1 School of Computer Science and Technology, ChangSha University of Science and Technology, Changsha 410114, China;
    2 School of Physics and Electronic Science, ChangSha University of Science and Technology, Changsha 410114, China 3 School of Information Engineering, Changsha Medical University, Changsha 410219, China
  • Received:2025-08-06 Revised:2025-08-20 Accepted:2025-08-26 Published:2025-12-10
  • Contact: Jie jin E-mail:jj67123@hnust.edu.cn
  • Supported by:
    This project was supported by the Guiding Science and Technology Plan Project of Changsha City under Grant kzd2501129, by the Natural Science Foundation of Hunan Province (Grant No. 2025JJ50368), the Scientific Research Fund of Hunan Provincial Education Department (Grant No. 24A0248), and the National Natural Science Foundation of China (Grant No. 62273141).

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摘要： The functionality of the biological brain is closely related to the dynamic behavior generated by synapses in its complex neural system. The self-connection synapse, as a critical form of feedback synapse in Hopfield neurons, plays an essential role in understanding the dynamic behavior of the brain. Synaptic memristors can bring neural network models closer to the complexity of the brain’s neural networks. Inspired by this, this study incorporates the nonlinear memory characteristics of synapses into the Hopfield neural network (HNN) by replacing a single self-synapse in a four-dimensional HNN model with a novel cosine memristor model, aiming to more realistically reproduce the dynamical behavior of biological neurons in artificial systems. By performing a dynamical analysis of the system using numerical methods, we find that the model exhibits infinitely many equilibrium points and can induce the formation of rare transient attractors, as well as an arbitrary number of multi-scroll attractors. Additionally, the model demonstrates complex coexisting attractor dynamics, including transient chaos, periodicity, decaying periodicity, and coexisting chaos. Furthermore, the feasibility of the proposed HNN model is verified using a field-programmable gate array (FPGA). Finally, an electronic codebook (ECB)-mode block cipher encryption algorithm is proposed for image encryption. The encryption performance is evaluated, with an information entropy value of 7.9993, demonstrating the excellent randomness of the system-generated numbers.

关键词: self-connected synapses, Hopfield neural network, multi-scroll attractor, field programmable gate array, image encryption

Abstract: The functionality of the biological brain is closely related to the dynamic behavior generated by synapses in its complex neural system. The self-connection synapse, as a critical form of feedback synapse in Hopfield neurons, plays an essential role in understanding the dynamic behavior of the brain. Synaptic memristors can bring neural network models closer to the complexity of the brain’s neural networks. Inspired by this, this study incorporates the nonlinear memory characteristics of synapses into the Hopfield neural network (HNN) by replacing a single self-synapse in a four-dimensional HNN model with a novel cosine memristor model, aiming to more realistically reproduce the dynamical behavior of biological neurons in artificial systems. By performing a dynamical analysis of the system using numerical methods, we find that the model exhibits infinitely many equilibrium points and can induce the formation of rare transient attractors, as well as an arbitrary number of multi-scroll attractors. Additionally, the model demonstrates complex coexisting attractor dynamics, including transient chaos, periodicity, decaying periodicity, and coexisting chaos. Furthermore, the feasibility of the proposed HNN model is verified using a field-programmable gate array (FPGA). Finally, an electronic codebook (ECB)-mode block cipher encryption algorithm is proposed for image encryption. The encryption performance is evaluated, with an information entropy value of 7.9993, demonstrating the excellent randomness of the system-generated numbers.

Key words: self-connected synapses, Hopfield neural network, multi-scroll attractor, field programmable gate array, image encryption

中图分类号:  (Nonlinear dynamics and chaos)

  • 05.45.-a
05.45.Gg (Control of chaos, applications of chaos) 07.05.Mh (Neural networks, fuzzy logic, artificial intelligence) 87.19.lj (Neuronal network dynamics)