Many neurons exhibit much more complicated firing patterns than the simple repetitive firing we have described here. Bursting, clustering of spikes followed by relative quiescence, is a common mode of firing in neurons and other excitable cells (see  for a brief review). Bursting cannot happen in two-variable models. The slow modulation of spiking during a burst requires additional biophysical mechanisms and dynamic variables. Moreover, just from mathematical considerations, a slowly drifting spike trajectory that recurs would violate the rule that trajectories in the phase plane cannot cross. However, we can build on our idealized two-variable model by adding a slow process and then use it to understand bursting from a simple geometric point of view. In this treatment a slow variable is first viewed as a parameter so that one describes the behavioral regimes of the fast spike-generating kinetics. Then the slow dynamics is overlaid as the full system sweeps through regimes of spiking and quiescence. Unless we state otherwise, bursting for us will imply repetitive bursting.