  Non-autonomous dynamical systems help us to understand the implications of
real systems which are in contact with their environment as it actually occurs
in nature. Here, we focus on systems where a parameter changes with time at
small but non-negligible rates before settling at a stable value, by using the
Lorenz system for illustration. This kind of systems commonly show a long-term
transient dynamics previous to a sudden transition to a steady state. This can
be explained by the crossing of a bifurcation in the associated frozen-in
system. We surprisingly uncover a scaling law relating the duration of the
transient to the rate of change of the parameter for a case where a chaotic
attractor is involved. Additionally, we analyze the viability of recovering the
transient dynamics by reversing the parameter to its original value, as an
alternative to the control theory for systems with parameter drifts. We obtain
the relationship between the paramater change rate and the number of
trajectories that tip back to the initial attractor corresponding to the
transient state.
