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 is the fast variable that simulates fast spiking of the neuron, and is the slow variable that modulates such spiking activity.
A topological classification of bursters relies on the bifurcations of the fast subsystem (variable ) when the slow subsystem (variable ) is treated as a parameter.
Izhikevich E.M. (2007) Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting. The MIT Press.
Eugene M. Izhikevich (2006) Bursting. Scholarpedia, p.1401 (available online at http://www.scholarpedia.org/article/Bursting).