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<p>The unique nonlinear and memory characteristics of memristors make them ideal devices for mimicking biological neural synapses, providing a critical foundation for the bio-inspired design of artificial neural networks. In this work, a single-memristor Hopfield neural network (SM-HNN) and two multi-memristor Hopfield neural network (MM-HNN) models with different numbers of memristors are proposed, and in-depth investigations of their dynamical behaviors and engineering applications are also conducted. All of the proposed SM-HNN and MM-HNN models employ a parsimonious three-neuron architecture, enabling flexible regulation of the direction and quantity of double-scroll attractors through the application of external excitatory currents of the memristors. Firstly, the study establishes a single-memristor coupled synaptic HNN model, which generates unidirectional double-scroll attractors controlled by memristor parameters. Based on nonlinear dynamics theory, the equilibrium point distribution of the model is systematically analyzed, and other methods such as phase portraits, bifurcation diagrams, and Lyapunov exponent spectra are also used to reveal the characteristics of its numerically controllable double-scroll chaotic attractors. Building on the above single-memristor model, two types of multi-memristor coupled synaptic HNN models are further designed. By tuning the memristor parameters, these new models can generate grid-like and spatial double-scroll attractors with fully controllable quantities. To validate the theoretical analysis, experiments are conducted using a field-programmable gate array (FPGA)-based digital hardware platform, confirming the consistency of the experiments with simulation results. Moreover, the proposed MM-HNN model is successfully applied to the field of information encryption, and it provides a novel technological pathway for information encryption by using its complex chaotic dynamical characteristics, effectively enhancing the security and reliability of encryption systems.</p>

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Design and realization of pulse-controlled multi-memristor Hopfield neural networks and their applications in information encryption

  • 期刊论文

  • 发表日期：

    2025年10月10日

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  • Zhenyao Li,
  • Jie Jin,
  • Daobing Zhang,
  • Chaoyang Chen

摘要

The unique nonlinear and memory characteristics of memristors make them ideal devices for mimicking biological neural synapses, providing a critical foundation for the bio-inspired design of artificial neural networks. In this work, a single-memristor Hopfield neural network (SM-HNN) and two multi-memristor Hopfield neural network (MM-HNN) models with different numbers of memristors are proposed, and in-depth investigations of their dynamical behaviors and engineering applications are also conducted. All of the proposed SM-HNN and MM-HNN models employ a parsimonious three-neuron architecture, enabling flexible regulation of the direction and quantity of double-scroll attractors through the application of external excitatory currents of the memristors. Firstly, the study establishes a single-memristor coupled synaptic HNN model, which generates unidirectional double-scroll attractors controlled by memristor parameters. Based on nonlinear dynamics theory, the equilibrium point distribution of the model is systematically analyzed, and other methods such as phase portraits, bifurcation diagrams, and Lyapunov exponent spectra are also used to reveal the characteristics of its numerically controllable double-scroll chaotic attractors. Building on the above single-memristor model, two types of multi-memristor coupled synaptic HNN models are further designed. By tuning the memristor parameters, these new models can generate grid-like and spatial double-scroll attractors with fully controllable quantities. To validate the theoretical analysis, experiments are conducted using a field-programmable gate array (FPGA)-based digital hardware platform, confirming the consistency of the experiments with simulation results. Moreover, the proposed MM-HNN model is successfully applied to the field of information encryption, and it provides a novel technological pathway for information encryption by using its complex chaotic dynamical characteristics, effectively enhancing the security and reliability of encryption systems.