  Studies of dynamical stability (chaotic versus regular motion) in galactic
dynamics often rely on static analytical models of the total gravitational
potential. Potentials based upon self-consistent N-body simulations offer more
realistic models, fully incorporating the time-dependent nature of the systems.
Here we aim at analysing the fractions of chaotic motion within different
morphological components of the galaxy. We wish to investigate how the presence
of chaotic orbits evolves with time, and how their spatial distribution is
associated with morphological features of the galaxy. We employ a
time-dependent analytical potential model that was derived from an N-body
simulation of a strongly barred galaxy. With this analytical potential we may
follow the dynamical evolution of ensembles of orbits. Using the Generalized
Alignment Index (GALI) chaos detection method, we study the fraction of chaotic
orbits, sampling the dynamics of both the stellar disc and of the dark matter
halo. Within the stellar disc, the global trend is for chaotic motion to
decrease in time, specially in the region of the bar. We scrutinized the
different changes of regime during the evolution (orbits that are permanently
chaotic, permanently regular, those that begin regular and end chaotic, and
those that begin chaotic and end regular), tracing the types of orbits back to
their common origins. Within the dark matter halo, chaotic motion also
decreases globally in time. The inner halo (r < 5 kpc) is where most chaotic
orbits are found and it is the only region where chaotic orbits outnumber
regular orbits, in the early evolution.
