Are external perturbations responsible for chaotic motion in galaxies?

Highlights: → The motion in a logarithmic potential with an additional external perturbation is studied. → Responsible for chaos is the external perturbation combined with the dense nucleus. → Numerical relationships connecting the dynamical parameter of the system are obtained. → A time-dependent model for the evolution of the stellar system is introduced and used. - Abstract: 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.