  We study the nature of motion in a logarithmic galactic dynamical model, with
an additional external perturbation. Two different cases are investigated. In
the first case the external perturbation is fixed, while in the second case it
is varying with the time. Numerical experiments suggest, that responsible for
the chaotic phenomena is the external perturbation, combined with the dense
nucleus. Linear relationships are found to exist, between the critical value of
the angular momentum and the dynamical parameters of the galactic system that
is, the strength of the external perturbation, the flattening parameter and the
radius of the nucleus. Moreover, the extent of the chaotic regions in the phase
plane, increases linearly as the strength of the external perturbation and the
flattening parameter increases. On the contrary, we observe that the percentage
covered by chaotic orbits in the phase plane, decreases linearly, as the scale
length of the nucleus increases, becoming less dense. Theoretical arguments are
used to support and explain the numerically obtained outcomes. A comparison of
the present outcomes with earlier results is also presented.
