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Model Neurons of Bifurcation Type 2

  • Christoph Börgers
Chapter
Part of the Texts in Applied Mathematics book series (TAM, volume 66)

Abstract

A neuron is said to be of bifurcation type 2 if the transition that occurs as I crosses I c is a Hopf bifurcation [47, 75, 129]. Examples of model neurons of bifurcation type 2 include the classical Hodgkin-Huxley model, and the Erisir model described in Section  5.3 The Hopf bifurcation in the classical Hodgkin-Huxley model is analyzed in great detail in [67]. For numerical evidence that the transition from rest to firing in the Erisir model involves a subcritical Hopf bifurcation, see [17], and also Fig.  17.9.

Supplementary material

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Bibliography

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    C. Börgers and B. Walker, Toggling between gamma-frequency activity and suppression of cell assemblies, Frontiers in Computational Neuroscience, 7, doi: 10.3389/fncom.2013.00033 (2013).Google Scholar
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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Christoph Börgers
    • 1
  1. 1.Department of MathematicsTufts UniversityMedfordUSA

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