We extend the one-dimensional, two-zone models of long-term protostellar disk evolution with infall of Zhu et al. to consider the potential effects of a finite viscosity in regions where the ionization is too low for the magnetorotational instability (MRI) to operate (the dead zone). We find that the presence of a small but finite dead zone viscosity, as suggested by simulations of stratified disks with MRI-active outer layers, can trigger inside-out bursts of accretion, starting at or near the inner edge of the disk, instead of the previously-found outside-in bursts with zero dead zone viscosity, which originate at a few AU in radius. These inside-out bursts of accretion bear a qualitative resemblance to the outburst behavior of one FU Ori object, V1515 Cyg, in contrast to the outside-in burst models which more closely resemble the accretion events in FU Ori and V1057 Cyg. Our results suggest that the type and frequency of outbursts are potentially a probe of transport efficiency in the dead zone. Simulations must treat the inner disk regions, $R lesssim 0.5$ AU, to show the detailed time evolution of accretion outbursts in general and to observe the inside-out bursts in particular.
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