Previous studies have observed that electromagnetic induction can seriously affect the electrophysiological activity of the nervous system. Considering the role of astrocytes in regulating neural firing, we studied a simple neuron-astrocyte coupled system under electromagnetic induction in response to different types of exteal stimulation. Both the duration and intensity of the exteal stimulus can induce different modes of electrical activity in this system, and thus the neuronal firing pattes can be subtly controlled. When the exteal stimulation ceases, the neuron will continue to fire for a long time and then reset to its resting state. In this study,"delay"is defined as the delayed time from the firing state to the resting state, and it is highly sensitive to changes in the duration or intensity of the exteal stimulus. Meanwhile, the self-similarity embodied in the aforementioned sensitivity can be quantified by fractal dimension. Moreover, a hysteresis loop of calcium activity in the astrocyte is observed in the specific interval of the exteal stimulus when the stimulus duration is extended to infinity, since astrocytic calcium or neuron electrical activity in the resting state or during periodic oscillation depends on the initial state. Finally, the regulating effect of electromagnetic induction in this system is considered. It is clarified that the occurrence of"delay"depends purely on the existence of electromagnetic induction. This model can reveal the dynamic characteristics of the neuron-astrocyte coupling system with magnetic induction under exteal stimulation. These results can provide some insights into the effects of electromagnetic induction and stimulation on neuronal activity.