{"title":"A novel memristive Hopfield neural network with grid attractor and its application in image encryption","authors":"Anna Guo, Chunlei Fan","doi":"10.1016/j.physa.2025.131005","DOIUrl":null,"url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":20152,"journal":{"name":"Physica A: Statistical Mechanics and its Applications","volume":"679 ","pages":"Article 131005"},"PeriodicalIF":3.1000,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physica A: Statistical Mechanics and its Applications","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0378437125006570","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
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.
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.