As we all know, various neuronal firing patterns carries different stimulus information. Based on a model of the isolated pancreatic β-cell, we investigated the bifurcation diagrams of interspike intervals (ISIs) and minimum action potentials, which clearly demonstrated the transitions between different firing patterns. The numerical simulation results revealed the effect of different time constants and iron channels on the neuronal discharge rhythm. On the one hand, an individual cell exhibited tonic spiking, square-wave bursting, and tapered bursting. On the other hand, several bifurcation phenomena can be observed in this paper, such as period-doubling, period-adding, inverse period-doubling and inverse period-adding scenarios.