A Fractional-Order Memristive Hopfield Neural Network and Its Application in Medical Image Encryption

With the rapid development of internet technologies, enhancing security protection for patient information during its transmission has become increasingly important. Compared with traditional image encryption methods, chaotic image encryption schemes leveraging sensitivity to initial conditions and pseudo-randomness demonstrate superior suitability for high-security-demand scenarios like medical image encryption. In this paper, a novel 3D fractional-order memristive Hopfield neural network (FMHNN) chaotic model with a minimum number of neurons is proposed and applied in medical image encryption. The chaotic characteristics of the proposed FMHNN model are systematically verified through various dynamical analysis methods. The parameter-dependent dynamical behaviors of the proposed FMHNN model are further investigated using Lyapunov exponent spectra, bifurcation diagrams, and spectral entropy analysis. Furthermore, the chaotic behaviors of the proposed FMHNN model are successfully implemented on FPGA hardware, with oscilloscope observations showing excellent agreement with numerical simulations. Finally, a medical image encryption scheme based on the proposed FMHNN model is designed, and comprehensive security analyses are conducted to validate its security for medical image encryption. The analytical results demonstrate that the designed encryption scheme based on the FMHNN model achieves high-level security performance, making it particularly suitable for protecting sensitive medical image transmission.