Abstract: During the modeling and analysis of neuronal activity, several biophysical effects should be taken into consideration. Due to fluctuations in intracellular and extracellular ion concentrations within the nervous system, internal fluctuations of electromagnetic fields and the effects of transmembrane magnetic flux need to be considered in the collective electrical activity and signal propagation between neuronal clusters. In this paper, a magnetic flux variable is introduced into a hybrid neuron, and a complex time-varying electromagnetic field is induced by modulating the membrane potential. Using analytical tools such as Xppauto, Matcont and Matlab, the existence and initial value of the equilibrium point of the new model, sensitivity and two-parameter bifurcation are discussed. When the external stimulus current and electromagnetic field change, the new model can be induced to generate abundant discharge modes, such as resting state, spike discharge, periodic (or chaotic) cluster discharge, especially coexisting discharge and hidden discharge benefited from the introduction of magnetic flux variable and memristor. According to the above analysis, the neuron model based on electromagnetic induction has high nonlinearity and more sensitive parameters, which enables the encryption algorithm to have a large key space. Based on this, an image encryption algorithm is designed in this paper. Pixels are first diffused once and then scrambled twice to their positions. Finally, through a series of numerical experiments, it is proved that the designed encryption algorithm can encrypt images effectively and has high security. The research takes into account the electromagnetic induction effect inside and outside the nerve cells, which is helpful for a more comprehensive understanding of the information encoding and transition laws between neurons. More bifurcation parameters and high complexity also make the designed neuron model has a good application prospect in image encryption.