Dynamical analysis of an improved memristive FHN neuron model and its application in medical image encryption

The electrical activity of neurons forms the foundation for a wide range of cognitive functions in the brain, and electromagnetic induction can significantly influence neuronal firing characteristics and information processing capabilities. Firstly, an improved memristive FitzHugh–Nagumo (m-FHN) neuron model under magnetic field modulation is proposed, which exhibits the coexistence of chaotic and periodic attractors. Numerical analysis of the Hamilton energy reveals a close relationship between neuronal firing patterns and energy levels. Secondly, the complex and variable dynamic behaviors of the model are thoroughly investigated using one-parameter bifurcation diagrams, one-parameter Lyapunov exponent spectra, spectral entropy complexity, two-parameter bifurcation diagrams, and two-parameter Lyapunov exponent spectra. In addition, the application of the model in medical image encryption is explored. By exploiting compressive sensing technology, a compression and encryption scheme is developed for the simultaneous encryption of multiple medical images, aiming to enhance the security and resource utilization efficiency of medical image transmission. The encryption algorithm integrates image fusion, compressive computation, diffusion, and permutation mechanisms. The initial conditions of the model are derived from the SHA-512 hash value of the original image, significantly improving resistance to differential attacks. Finally, numerical simulations and security experiment results confirm the effectiveness of the encryption scheme.