  In this paper we revise the model proposed by Rein et al. (2010) for the
origin of the HD45364 exoplanetary system, currently known to host two planets
close to the 3/2 mean-motion commensurability (MMR). We show that, due to high
surface density of the protoplanetary disk needed for Type III migration, this
model could only lead to planets in a quasi-resonant regime of motion, and thus
not consistent with the resonant configuration obtained by Correia et al.
(2009). Although both resonant and quasi-resonant solutions are statistically
indistinguishable with respect to radial velocity measurements, their distinct
dynamical behaviour is intriguing. We use the semi-analytical model to confirm
the quantitative difference between two configurations. In order to form a
system evolving inside the 3/2 resonance, we develop a different model. Our
scenario includes an interaction between different (but slower) planetary
migration types, planet growth, and gap formation in the protoplanetary disk.
The choice of the described evolutionary path was due to a detailed analysis of
the structure of the phase space in the vicinity of the 3/2 MMR employing
dynamical mapping techniques. The outcomes of our simulations are able to
reproduce very closely the 3/2 resonant dynamics obtained from the best-fit
presented by Correia et al. (2009). In addition, varying the strength of the
eccentricity damping, we can also simulate the quasi-resonant configuration
similar to that in Rein et al. (2010). We furthermore show that our scenario is
robust with respect to the physical parameters involved in the resonance
trapping process. However, the confirmation of our scenario will be possible
only with additional radial velocities measurements.
