  In this paper we consider the rate of convergence of solutions of a scalar
ordinary differential equation which is a perturbed version of an autonomous
equation with a globally stable equilibrium. Under weak assumptions on the
nonlinear mean reverting force, we demonstrate that the convergence rate is
preserved when the perturbation decays more rapidly than a critical rate. At
the critical rate, the convergence to equilibrium is slightly slower than the
unperturbed equation, and when the perturbation decays more slowly than the
critical rate, the convergence to equilibrium is strictly slower than that seen
in the unperturbed equation. In the last case, under strengthened assumptions,
a new convergence rate is recorded which depends on the convergence rate of the
perturbation. The latter result relies on the function being regularly varying
at the equilibrium with index greater than unity; therefore, for this class of
regularly varying problems, a classification of the convergence rates is
obtained.
