A model of neuro-astrocytic coupling with electromagnetic induction has been developed to deeply investigate the genesis and propagation of Delay within networks. Delay is defined as the time neurons continue to fire after external stimulation has ceased until they reach a resting state. The findings reveal that the primary cause of Delay in the neuron-astrocyte coupling system is the role of astrocytes. We observe that within a certain range, the feedback intensity causes a fractal structure of Delay, and as the feedback from astrocytes intensifies, Delay increases indefinitely. Neurons can continue firing indefinitely post-stimulation, and we have identified the feedback threshold for this infinite Delay. Further, we observed the transmission of Delay in neuron-astrocyte networks. Subsequent neurons, which would not normally fire, begin to discharge during the transmission of Delay, a phenomenon induced by either synaptic or astrocytic coupling. Finally, with electromagnetic induction, we noted the cumulative effect of Delay in the network, leading to longer sustained firing in more distant neurons as the network extends and propagates. Our research elucidates the precise mechanisms of generation and propagation of Delay, offering insights akin to mechanisms of memory in the nervous system, potentially providing novel understandings in the field of cognitive science.