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Pre-Botzinger complex is considered to have a closely relationship with the respiratory rhythms. In this paper, we investigate the bursting phenomena of the pre-Botzinger complex respiratory neuron with periodic slow stimulation. Since the external forcing visit the spiking and rest areas in different ways, thus the system could generate various complex bursting patterns. With the external forcing is taken as a slow variable that modulates the dynamics of the system, different types of bursting are distinguished and the generation mechanism is explored by using the combination of two parameter bifurcation analysis and fast slow decomposition. Our results show that both the external forcing and the neural intrinsic property play an important role in neural activities.