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
$$\begin{array}{cc}\hfill \dot{x}=f(x,y)\hfill & \hfill \text{(fast spiking)}\hfill \\ \hfill \dot{y}=\mu g(x,y)\hfill & \hfill \text{(slow modulation)}\hfill \end{array}$$ |
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 |
---|---|
Canonical name | Bursting |
Date of creation | 2013-03-22 16:28:51 |
Last modified on | 2013-03-22 16:28:51 |
Owner | emi (15656) |
Last modified by | emi (15656) |
Numerical id | 7 |
Author | emi (15656) |
Entry type | Definition |
Classification | msc 92B20 |
Classification | msc 92C20 |
Synonym | burst |