Model Neurons of Bifurcation Type 3

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


In neuronal models of bifurcation type 2 (Chapter  14), the possibility of stable rest is abolished via a Hopf bifurcation as I rises above I c , and the possibility of stable periodic firing is abolished via a collision of the stable limit cycle with an unstable periodic orbit as I falls below I, with I < I c . In neuronal models of bifurcation type 1 (Chapter  12), there is no distinction between I and I c ; stable rest is abolished as I rises above I c , and stable periodic firing is abolished as I falls below I c .


Hopf Bifurcation Model Neuron Sodium Current Stable Limit Cycle Stable Node 
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© Springer International Publishing AG 2017

Authors and Affiliations

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

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