How the SGL of a spiking neuron behaves approximately as a voltage-to-frequency converter (VFC), driven by a (positive) generator potential (GP) that is the spatiotemporal sum of epsps and ipsps has been described. As seen from the discussion of the HH model equations in Section 1.4, spike generation is a nonlinear process. There is a minimum GP below which a neuron will not fire, and the steady-state spike frequency is a nonlinear saturating function of the GP.
To model spike generation heuristically on a computer, there are two mathematical models that are considerably simpler than the HH equations. The simpler model for action potential generation as a function of a GP is called integral pulse frequency modulation (IPFM) (Li, 1961; Meyer, 1961; Pavlidis, 1964). A more realistic SGL model uses relaxation pulse frequency modulation (RPFM), in which the integrator is replaced with a simple, one-pole low-pass filter (Meyer, 1961). The properties and simulation of these simple SGL models are described below.
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