  We investigated the boundary between stable and unstable regimes of accretion
and its dependence on different parameters. Simulations were performed using a
"cubed sphere" code with high grid resolution (244 grid points in the azimuthal
direction), which is twice as high as that used in our earlier studies. We
chose a very low viscosity value, with alpha-parameter alpha=0.02. We observed
from the simulations that the boundary strongly depends on the ratio between
magnetospheric radius r_m (where the magnetic stress in the magnetosphere
matches the matter stress in the disk) and corotation radius r_cor (where the
Keplerian velocity in the disk is equal to the angular velocity of the star).
For a small misalignment angle of the dipole field, Theta=5 degrees, accretion
is unstable if r_cor/r_m>1.35, and is stable otherwise. In cases of a larger
misalignment angle of the dipole, Theta=20 degrees, instability occurs at
slightly larger values, r_cor/r_m>1.41.
