Knowledge of intrinsic neuronal firing dynamics is a critical first step to establishing an accurate biophysical model of any neuron. In this study we examined cerebellar Purkinje cells to determine the bifurcations likely to underlie firing dynamics within a biophysically realistic and experimentally supported model. We show that Purkinje cell dynamics are consistent with a system undergoing a saddle-node bifurcation of fixed points in the transition from rest to firing, and a saddle homoclinic bifurcation from firing to rest. Our analyses account for numerous observed Purkinje cell firing properties that include bistability, plateau potentials, specific aspects of the frequency-current (F-I) relationship, first spike latency, and the ability for climbing fiber input to induce state transitions in the bistable regime. We also experimentally confirm new properties predicted from our model and analysis that include the presence of a depolarizing afterpotential (DAP), the ability to fire at low frequencies (< 50 Hz) and with a high gain in the F-I relationship, and a bistable region limited to low frequency firing. Purkinje cell dynamics, including bistability, prove to arise from numerous biophysical factors that include the DAP, fast refractory dynamics and a long membrane time constant. A hyperpolarizing activated cation current (I_H) is shown not to be directly involved in establishing bistable dynamics but rather reduces the range for bistability. A combined electrophysiological and modeling approach thus accounts for several properties of Purkinje cells, providing a firm basis from which to assess Purkinje cell output patterns.