  Self-consistent N-body simulations are efficient tools to study galactic
dynamics. However, using them to study individual trajectories (or ensembles)
in detail can be challenging. Such orbital studies are important to shed light
on global phase space properties, which are the underlying cause of observed
structures. The potentials needed to describe self-consistent models are
time-dependent. Here, we aim to investigate dynamical properties
(regular/chaotic motion) of a non-autonomous galactic system, whose
time-dependent potential adequately mimics certain realistic trends arising
from N-body barred galaxy simulations. We construct a fully time-dependent
analytical potential, modeling the gravitational potentials of disc, bar and
dark matter halo, whose time-dependent parameters are derived from a
simulation. We study the dynamical stability of its reduced time-independent
2-degrees of freedom model, charting the different islands of stability
associated with certain orbital morphologies and detecting the chaotic and
regular regions. In the full 3-degrees of freedom time-dependent case, we show
representative trajectories experiencing typical dynamical behaviours, i.e.,
interplay between regular and chaotic motion for different epochs. Finally, we
study its underlying global dynamical transitions, estimating fractions of
(un)stable motion of an ensemble of initial conditions taken from the
simulation. For such an ensemble, the fraction of regular motion increases with
time.
