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Bursting and Adaptation: Spiking Dynamics with Slow Modulation.

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.

Bard Ermentrout
Mon Jul 29 17:47:46 EDT 1996