A variety of firing rhythms can be generated spontaneously in the pre-Bötzinger complex. External stimuli can cause changes in the pattern of the firing rhythm, which may cause different physiological effects in the body. In this study, by the fast and slow time scale dynamics, with one- and two-parameter bifurcation analysis, we study the bursting patterns and their transition mechanisms of the pre-Bötzinger complex under washout filter controller. The results may help us understand the relationship between different firing patterns of neurons and external stimuli, and further reveal the mechanisms of disease due to external stimuli.
