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
[36] 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.

- Square-wave Bursters
- Chaos and Poincare Maps.
- Elliptic Bursters.
- Parabolic Bursting: Two Slow Processes.

Mon Jul 29 17:47:46 EDT 1996