Spike initiation & time-dependent threshold changes

[Christof Koch]

The fact that the threshold of firing goes up following action potential dischar
ge
is a well know and well studied model. It's paartially caused by the influx of
calcium, which activates one or two calcium-dependent potassium currents.
 
See the model in Chapter 4 ("Multiple channels and calcium dynamics" in
the book "Methods in Neuronal Modeling", (C. Koch and I. Segev, eds.),
MIT Press, 1989. This book contains a number of quite detailed, state-of-the-art
 
models. One of the best studied models of spike-initiation is still the
integrate-and-fire or leaky-integrate-and-fire models, develoepd by Brice
Knight. It's quite well described in Tuckwell's two volume monograph
"Introduction to theoretical neurobiology" (Cambridge Univ. Press, 1988).
 
Some analytical solutions are known, for instance in the case that the
input is a Poisson input.
 
Christof