Qualitative and numerical analysis of a cosmological model based on an asymmetric scalar doublet with minimal couplings. II. Numerical modeling of phase trajectories. With the help of our own software package DifEqTools, numerical modeling of the cosmological evolution of a system consisting of an asymmetric scalar doublet of nonlinear, minimally interacting scalar fields, a classical field and a phantom field, has been performed. Peculiarities of the behavior of the model near zeroenergy hypersurfaces have been revealed.