  We use an extension of the van der Pol oscillator as an example of a system
with multiple time scales to study the susceptibility of its trajectory to
polynomial perturbations in the dynamics. A striking feature of many nonlinear,
multi-parameter models is an apparently inherent insensitivity to large
magnitude variations in certain linear combinations of parameters. This
phenomenon of "sloppiness" is quantified by calculating the eigenvalues of the
Hessian matrix of the least-squares cost function which typically span many
orders of magnitude. The van der Pol system is no exception: Perturbations in
its dynamics show that most directions in parameter space weakly affect the
limit cycle, whereas only a few directions are stiff. With this study we show
that separating the time scales in the van der Pol system leads to a further
separation of eigenvalues. Parameter combinations which perturb the slow
manifold are stiffer and those which solely affect the transients in the
dynamics are sloppier.
