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

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.