It is a well established fact that some YSO jets (e.g. RW Aur) display different propagation speeds between their blue and red shifted parts, a feature possibly associated with the central engine or the environment in which the jet propagates. In order to understand the origin of asymmetric YSO jet velocities, we investigate the efficiency of two candidate mechanisms, one based on the intrinsic properties of the system and one based on the role of the external medium. In particular, a parallel or anti-parallel configuration between the protostellar magnetosphere and the disk magnetic field is considered and the resulting dynamics are examined both in an ideal and a resistive magneto-hydrodynamical (MHD) regime. Moreover, we explore the effects of a potential difference in the pressure of the environment, as a consequence of the non-uniform density distribution of molecular clouds. Ideal and resistive axisymmetric numerical simulations are carried out for a variety of models, all of which are based on a combination of two analytical solutions, a disk wind and a stellar outflow. We find that jet velocity asymmetries can indeed occur both when multipolar magnetic moments are present in the star-disk system as well as when non-uniform environments are considered. The latter case is an external mechanism that can easily explain the large time scale of the phenomenon, whereas the former one naturally relates it to the YSO intrinsic properties. [abridged]
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