  Aims and Methods. Accretion bursts triggered by the magnetorotational
instability (MRI) in the innermost disk regions were studied for protoplanetary
gas-dust disks formed from prestellar cores of various mass $M_{\rm core}$ and
mass-to-magnetic flux ratio $\lambda$. Numerical magnetohydrodynamics
simulations in the thin-disk limit were employed to study the long-term ($\sim
1.0$~Myr) evolution of protoplanetary disks with an adaptive turbulent
$\alpha$-parameter, which depends explicitly on the strength of the magnetic
field and ionization fraction in the disk. The numerical models also feature
the co-evolution of gas and dust, including the back-reaction of dust on gas
and dust growth. Results. Dead zone with a low ionization fraction $x <=
10^{-13}$ and temperature on the order of several hundred Kelvin forms in the
inner disk soon after its formation, extending from several to several tens of
astronomical units depending on the model. The dead zone features pronounced
dust rings that are formed due to the concentration of grown dust particles in
the local pressure maxima. Thermal ionization of alkaline metals in the dead
zone trigger the MRI and associated accretion burst, which is characterized by
a sharp rise, small-scale variability in the active phase, and fast decline
once the inner MRI-active region is depleted of matter. The burst occurrence
frequency is highest in the initial stages of disk formation, and is driven by
gravitational instability (GI), but declines with diminishing disk mass-loading
from the infalling envelope. There is a causal link between the initial burst
activity and the strength of GI in the disk fueled by mass infall from the
envelope. Abridged.
