A novel memristive Hopfield neural network with grid attractor and its application in image encryption

IF 3.1 3区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY
Anna Guo, Chunlei Fan
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引用次数: 0

Abstract

As a nonlinear resistor with memory characteristics, the memristor can simulate synaptic behavior in neural networks. Building upon the Hopfield neural network (HNN), this paper proposes a novel memristive HNN model by utilizing memristors to realize neuron self-synaptic connections. By adjusting the parameters of the memristor, chaotic attractors can be generated with different numbers and complex structures. The analysis of equilibrium points and stability elucidates the mechanism behind the emergence of multi-structure chaotic attractors. The dynamical characteristics are investigated through the Lyapunov exponent spectrum, bifurcation diagrams, time series, and basin of attraction. Based on the complex dynamics of the memristive HNN, we design a color image encryption scheme combining oblique diffusion and cross-channel Hilbert scanning. Oblique diffusion effectively achieves global propagation of pixel-level perturbations, while cross-channel Hilbert scanning breaks the pixel correlation within individual channels while enhancing inter-channel dependencies. Experimental results demonstrate that the algorithm exhibits extremely high key sensitivity and strong robustness, effectively resisting common attacks such as statistical analysis and differential attacks.
一种具有网格吸引子的记忆Hopfield神经网络及其在图像加密中的应用
忆阻器是一种具有记忆特性的非线性电阻器,可以模拟神经网络中的突触行为。在Hopfield神经网络(HNN)的基础上,提出了一种利用忆阻器实现神经元自突触连接的忆阻神经网络模型。通过调整忆阻器的参数,可以产生不同数量和复杂结构的混沌吸引子。平衡点和稳定性分析阐明了多结构混沌吸引子产生的机理。通过李雅普诺夫指数谱、分岔图、时间序列和引力盆地研究了其动力学特性。基于记忆HNN的复杂动态特性,设计了一种斜扩散与跨通道希尔伯特扫描相结合的彩色图像加密方案。斜向扩散有效地实现了像素级扰动的全局传播,而跨通道希尔伯特扫描则打破了单个通道内的像素相关性,同时增强了通道间的依赖性。实验结果表明,该算法具有极高的密钥灵敏度和较强的鲁棒性,能够有效抵御统计分析和差分攻击等常见攻击。
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来源期刊
CiteScore
7.20
自引率
9.10%
发文量
852
审稿时长
6.6 months
期刊介绍: Physica A: Statistical Mechanics and its Applications Recognized by the European Physical Society Physica A publishes research in the field of statistical mechanics and its applications. Statistical mechanics sets out to explain the behaviour of macroscopic systems by studying the statistical properties of their microscopic constituents. Applications of the techniques of statistical mechanics are widespread, and include: applications to physical systems such as solids, liquids and gases; applications to chemical and biological systems (colloids, interfaces, complex fluids, polymers and biopolymers, cell physics); and other interdisciplinary applications to for instance biological, economical and sociological systems.
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