Two and three dimensional reductions of the Hodgkin-Huxley system: separation of time scales and bifurcation schemes

@article{Meunier1992TwoAT,
  title={Two and three dimensional reductions of the Hodgkin-Huxley system: separation of time scales and bifurcation schemes},
  author={Claude Meunier},
  journal={Biological Cybernetics},
  year={1992},
  volume={67},
  pages={461-468}
}
We study two different two-dimensional reductions of the Hodgkin-Huxley equations. We show that they display the same qualitative bifurcation scheme as the original equations but overestimate the current range where periodic emission occurs. This is essentially due to the assumption that the evolution of the sodium activation variable m is instantaneous with respect to the dynamics of the variables h and n, an hypothesis that breaks down at high values of the injected current. To prove this… CONTINUE READING
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