Abstract: The change of ions inside and outside the cell will affect the change of cell membrane potential and produce the distribution of electromagnetic field. Pancreatic β cell neurons can be established based on the four-dimensional model of neuron membrane potential coupling between the magnetic flux which is realized by a memristor neurons, causing effect of the feedback gain k_1 of pancreatic β cells, the discharge mode, and to obtain different behaviors bifurcation corresponding conditions. The effects of external electrical stimulation I_\rmext on the firing pattern of neurons were investigated, and the appropriate parameters were selected for numerical simulation. The results show that there are periodic bifurcations in the system, and there is a transition between the inverse plus period bifurcation and the doubling bifurcation, showing the transition of the resting state- periodic spiking -chaos -periodic bursting discharge mode. The synchronization characteristics of the magnetic flux coupled pancreatic β-cells have been analyzed, and the synchronization difference principle is used to deduce the conditions for the system to reach the synchronization state. At the same time, the system is analyzed by two parameters. The analysis results show that when the system is in weak coupling strength, the system will gradually reach the synchronization state with the increase of coupling strength, which indicates that increasing the coupling strength under the weak coupling strength can promote the synchronization of the system. Increasing the coupling strength to a certain extent can not promote the synchronization of the system, and verify the relationship between the coupling strength and the synchronization of the system.