Bifurcation and multiple timescale dynamics of mixed bursting in the neuronal model

Neurons within the pre-Bötzinger complex have been found experimentally to exhibit different firing activities. Mixed bursting is a special firing activities which has been found in neuron model and biological experiments. The traditional fast and slow dynamics analysis method encounters some difficulties in analyzing mixed bursting. Therefore, how to analyze the dynamic mechanism of mixed bursting generation and transition is a very important issue. In this paper, based on fast-slow decomposition, multiple timescale dynamics and one- and two-parameter bifurcation analysis, we investigate the mixed bursting and their transition mechanisms in pre-Bötzinger complex neurons. The results show that the generation mechanism of the mixed bursting is related to the multiple timescale of the neuron model. The results obtained in this paper is instructive for further understanding the dynamical behaviours and generation mechanisms of complex firing activities in biological nervous systems.