Dynamics analysis of fractional-order extended neuron model under electromagnetic field and application to image encryption

In this paper, a novel five-dimensional fractional-order extended Hindmarsh–Rose neuron model under electromagnetic field (FEHREF) is established. Numerical analysis methods such as time series diagrams, phase diagrams and bifurcation portraits demonstrate that the proposed model can exhibit complex dynamic behaviors such as regular spiking, period bursting and chaotic firing, when the intensity of the external current input and the strength of the magnetic field effect are varied, respectively. Moreover, a gray image encryption algorithm based on the proposed FEHREF combined with extended DNA coding is presented. The extended DNA encoding scheme can add DNA coding rules to improve the security of the image encryption algorithm. Finally, the performance of the designed encryption algorithm is analyzed in detail. The experimental results verify that the proposed algorithm can resist multiple attacks with better performance and higher security. This work provides theoretical guidance and experimental foundation for image-secure communication by combining fractional-order neuron system with extended DNA coding.