Multi-stability involved mixed bursting within the coupled pre-Bötzinger complex neurons

Neurons in the pre-Bötzinger complex within the mammalian brain stem play important roles in the generation of respiratory rhythms. Experimental observations show that some neurons can exhibit novel mixed bursting activities. In this paper, based on a mathematical model proposed by Butera, we show how the mixed bursting activities depend on the potassium current in the coupled pre-Botzinger complex. Using fast-slow decomposition and bifurcation analysis, we investigate the dynamics of mixed bursting, as well as the mechanisms of transition between different mixed bursting patterns. We find that mixed bursting involves different bistability, and it is the transition state of two types of regular burstings.