Exploring the nature of orbits in a galactic model with a massive nucleus

► An axially symmetric galactic model with a disk-halo and a spherical nucleus is used. ► The galactic core hosts a dense and massive spherical nucleus. ► We reveal the structure of the dynamical system using a time independent model. ► We explore the nature of orbits in the case of the time evolving model. ► A theoretical analysis to support the numerically derived outcomes is also presented.