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<p>In neural networks, complex topological structures often lead to diverse dynamic behaviors. Therefore, a non-volatile locally active memristor is proposed, and a four-neuron Memristive Recurrent topology Hopfield Neural Network with Dual Self-Loops (MRHNN-DSL) is constructed by simulating the external electromagnetic radiation effect through the memristor. Numerical simulations reveal that the MRHNN-DSL exhibits a variety of symmetric coexisting attractors–such as chaotic, quasi-periodic, periodic, and fixed-point behaviors–within the parameter space. Further analysis indicates that when the memristive parameter falls within the locally active region, the MRHNN-DSL tends to converge, whereas in the non-locally active region, it predominantly exhibits divergent dynamics. In addition, the introduction of multi-level logic pulse current can significantly change the dynamic behavior of MRHNN-DSL, not only inducing multi-scroll attractors, but also the number of scrolls has an exponential relationship with the pulse level. The correctness and effectiveness of the theoretical model are validated through circuit experiments. Furthermore, based on the multistability of MRHNN-DSL, we propose a novel medical image encryption scheme that utilizes coordinate pair indices composed of self-orthogonal Latin squares and their transposed matrices to achieve simultaneous permutation and diffusion within the Galois field. This scheme reduces redundant operations and effectively enhances encryption speed. Meanwhile, the encryption scheme introduces an internal initial value mapping method that adaptively selects chaotic symmetric attractors from the MRHNN-DSL, substantially improving the randomness of the generated chaotic sequences. Security analysis shows that the medical image encryption scheme performs excellently in multiple key security performance indicators.</p>

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Recurrent Hopfield neural network under multiple stimuli and its application in medical image encryption

  • 期刊论文

  • 发表日期：

    2025年8月22日

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  • Zhi Huang,
  • Zhen Li,
  • Qiao Wang,
  • Weijie Tan,
  • Xianming Wu

摘要

In neural networks, complex topological structures often lead to diverse dynamic behaviors. Therefore, a non-volatile locally active memristor is proposed, and a four-neuron Memristive Recurrent topology Hopfield Neural Network with Dual Self-Loops (MRHNN-DSL) is constructed by simulating the external electromagnetic radiation effect through the memristor. Numerical simulations reveal that the MRHNN-DSL exhibits a variety of symmetric coexisting attractors–such as chaotic, quasi-periodic, periodic, and fixed-point behaviors–within the parameter space. Further analysis indicates that when the memristive parameter falls within the locally active region, the MRHNN-DSL tends to converge, whereas in the non-locally active region, it predominantly exhibits divergent dynamics. In addition, the introduction of multi-level logic pulse current can significantly change the dynamic behavior of MRHNN-DSL, not only inducing multi-scroll attractors, but also the number of scrolls has an exponential relationship with the pulse level. The correctness and effectiveness of the theoretical model are validated through circuit experiments. Furthermore, based on the multistability of MRHNN-DSL, we propose a novel medical image encryption scheme that utilizes coordinate pair indices composed of self-orthogonal Latin squares and their transposed matrices to achieve simultaneous permutation and diffusion within the Galois field. This scheme reduces redundant operations and effectively enhances encryption speed. Meanwhile, the encryption scheme introduces an internal initial value mapping method that adaptively selects chaotic symmetric attractors from the MRHNN-DSL, substantially improving the randomness of the generated chaotic sequences. Security analysis shows that the medical image encryption scheme performs excellently in multiple key security performance indicators.