bursting

In neuroscience, bursting denotes two or more action potentials (spikes) fired by a neuron, followed by a period of quiescence. A burst of two spikes is called a doublet, three spikes - triplet, four - quadruplet, etc.

Most mathematical models of bursting can be written in the singularly perturbed form

where $x\in {ℝ}^n$ is the fast variable that simulates fast spiking of the neuron, and $y\in {ℝ}^m$ is the slow variable that modulates such spiking activity.

A topological classification of bursters relies on the bifurcations of the fast subsystem (variable $x$) when the slow subsystem (variable $y$) is treated as a parameter.