  Nonlinear biophysical properties of individual neurons are known to play a
major role in the nervous system. Earlier electrophysiological studies have
made use of piecewise linear characterization of voltage clamped neurons, which
consists of a sequence of linear admittances computed at different voltage
levels. In this paper, the linear approach is extended to a piecewise quadratic
characterization in two different ways. First, an analytical model is derived
with power series following the work pionneered by Fitzhugh. Second, matrix
calculus is developed to provide a novel quantitative analysis not dependent on
differential equations. This method provides an assessment of quadratic
responses for both data recorded from individual neurons and their
corresponding models.
