Qualitative Bursting Models

To a large extent, all of the models discussed above are based on biophysical mechanisms, with the parameters and functions in the models derived from experimental data. An alternative approach is to construct a polynomial model that retains the important qualitative features but is simpler to analyze and understand (Hindmarsh and Rose, 1984; Pernarowski, 1994). Such a model has the same relationship to the above models as the FitzHugh-Nagumo model does to the Hodgkin-Huxley model: it is phe-nomenological in nature and based on the fact that the underlying behavior of the biophysical models can be distilled into a simpler model containing only polynomials.

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