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<p>This paper designs two improved passive cosine-type ideal memristors and incorporates them into the Hopfield neural network, thereby proposing a novel cosine-type memristor-driven Hopfield neural network (CMDHNN). The model exhibits a planar equilibrium set and demonstrates extreme multistability, characterized by the coexistence of infinitely many attractors. The boundedness of the system is rigorously proven using the Lyapunov method. Nonlinear dynamics analysis tools, including bifurcation diagrams, Lyapunov exponent spectra, phase portraits, and time series plots, are employed to thoroughly investigate the model’s complex chaotic dynamics. Leveraging the chaotic system of the proposed CMDHNN, an image encryption scheme is developed, in which chaotic sequences are utilized to generate diffusion and permutation key streams for encrypting the plaintext image. The results indicate that the encryption scheme based on this model exhibits excellent robustness and can effectively resist various common attacks.</p>

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Coexistence of infinitely many attractors in cosine-type memristor-driven hopfield neural networks and its application to image encryption

  • 期刊论文

  • 发表日期：

    2026年3月19日

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  • Xiaowei Yin,
  • Guangzhe Zhao,
  • Chengjie Chen,
  • Yunkai You,
  • Chunlong Zhou,
  • Yunzhen Zhang

摘要

This paper designs two improved passive cosine-type ideal memristors and incorporates them into the Hopfield neural network, thereby proposing a novel cosine-type memristor-driven Hopfield neural network (CMDHNN). The model exhibits a planar equilibrium set and demonstrates extreme multistability, characterized by the coexistence of infinitely many attractors. The boundedness of the system is rigorously proven using the Lyapunov method. Nonlinear dynamics analysis tools, including bifurcation diagrams, Lyapunov exponent spectra, phase portraits, and time series plots, are employed to thoroughly investigate the model’s complex chaotic dynamics. Leveraging the chaotic system of the proposed CMDHNN, an image encryption scheme is developed, in which chaotic sequences are utilized to generate diffusion and permutation key streams for encrypting the plaintext image. The results indicate that the encryption scheme based on this model exhibits excellent robustness and can effectively resist various common attacks.