One of the most important features of neurons is their ability to produce prominent responses (called action potential) upon excitation induced by supra-threshold stimuli. This phenomenon, labeled excitability, was first modeled by Hodgkin and Huxley in the 1950s and later triggered an avalanche of modeling studies investigating dynamically the role of various ion channels in producing such behaviour. In all of these studies, excitability was assumed to be constant in time, with no changes in the firing threshold or frequency. Our recent work, however, has shown that some neurons do alter their excitability over time after patch-clamping them. More specifically, we found that stellate cells of the cerebellum, involved in motor control, increase their excitability over time (runup) and exhibit peculiar latency profile (latency to firing). They achieve this by altering the kinetics of certain ion channels expressed on their membrane. Using mathematical modeling techniques, we identified what these ion channels are and how they alter their kinetics. In this talk, I will present a model that explains these outcomes and illustrate how we used dynamical systems approaches to explain the runup phenomenon in excitability and the biphasic profile in latency.