Effect of magnetic flow and external forcing current on mixed bursting in the pre-Bötzinger complex

The pre-Bötzinger complex (pre-BötC) in mammalian brainstem is essential for the generation of respiratory rhythms. Most dynamic studies on the pre-BötC neuron have been focused on its firing activities modulated by the ion conductances rather than that by the electromagnetic radiation or the external forcing current. In this paper, by adding the electromagnetic radiation and external forcing current to Park and Rubin’s model, we mainly investigate the influences of those two factors on the mixed bursting (MB) of single pre-BötC neuron. First, we explore how the variation of external forcing current affects the MB patterns of the system with non-vanishing magnetic flux. We classify the MB patterns and show their dynamic mechanism through fast-slow decomposition and bifurcation analysis. Then, by modifying the feedback coefficient, we further analyze the sole effect of electromagnetic radiation on the firing activities of the system. Our results may be instructive in understanding the dynamical behavior of pre-BötC neuron.