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This quadratic integrate-and-fire model corresponds to the normal form of a conductance-based neuron near a saddle-node bifurcation. It can be derived exactly in the limit of low firing rates. This is in contrast with the (linear) integrate-and-fire model [L. Lapicque, J. Physiol. (Paris) 9, 620 (1907)] which is frequently used. The variable X is adimensional. In a normal form analysis near the bifurcation it can be related to a linear combination of the voltage and gating variables.
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In the first situation, bistability between two active states can be possible.
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