Encyclopedia of Computational Neuroscience

Living Edition
| Editors: Dieter Jaeger, Ranu Jung

Bifurcations Dynamics of Single Neurons and Small Networks

Living reference work entry
DOI: https://doi.org/10.1007/978-1-4614-7320-6_453-1


A bifurcation occurs when a system undergoes a qualitative change in its output as a result of a change in parameter. Under certain conditions, the voltage of a cell membrane can change from being at rest to becoming oscillatory as a result of a bifurcation. Oscillatory properties of small networks are often understood using bifurcation analysis.


What Is a Bifurcation?

The word bifurcate is commonly used to denote a split, as in “up ahead, the road bifurcates into two parts.” The use of the term in this context implies that a driver traveling on this road can make a real-time choice of being able to take one or the other branch of the road when the bifurcation point is reached. In mathematics, and in its application to neuroscience, the term bifurcation has an entirely different contextual meaning. While a mathematical bifurcation is similar in that it involves different branches, the decision on which branch is chosen is largely made a priori and depends on the...


Periodic Orbit Hopf Bifurcation Bifurcation Diagram Bifurcation Analysis Pitchfork Bifurcation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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This work was supported in part by NSF DMS 1122291.


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© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Mathematical SciencesNew Jersey Institute of TechnologyNewarkUSA