# 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

 $\begin{matrix}\dot{x}=\ f(x,y)&\ \ \ \ \ \ \ \mbox{(fast spiking)}\\ \dot{y}=\mu g(x,y)&\mbox{(slow modulation)}\end{matrix}$

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

## References

• iz Izhikevich E.M. (2007) Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting. The MIT Press.
• izb Eugene M. Izhikevich (2006) Bursting. Scholarpedia, p.1401 (available online at http://www.scholarpedia.org/article/Bursting).
Title bursting Bursting 2013-03-22 16:28:51 2013-03-22 16:28:51 emi (15656) emi (15656) 7 emi (15656) Definition msc 92B20 msc 92C20 burst