  Here we analytically examine the response of a limit cycle solution to a
simple differential delay equation to a single pulse perturbation of the
piecewise linear nonlinearity. We construct the unperturbed limit cycle
analytically, and are able to completely characterize the perturbed response to
a pulse of positive amplitude and duration with onset at different points in
the limit cycle. We determine the perturbed minima and maxima and period of the
limit cycle and show how the pulse modifies these from the unperturbed case.
