  We perform global time-dependent simulations of an accretion disc around a
young stellar object with a dead zone (a region where the magneto-rotational
instability cannot drive turbulence because the material is not sufficiently
ionised). For infall accretion rates on to the disc of around 10^-7 Msun/yr,
dead zones occur if the critical magnetic Reynolds number is larger than about
10^4. We model the collapse of a molecular gas cloud. At early times when the
infall accretion rate is high, the disc is thermally ionised and fully
turbulent. However, as the infall accretion rate drops, a dead zone may form if
the critical magnetic Reynolds number is sufficiently large, otherwise the disc
remains fully turbulent. With a dead zone the disc can become unstable to the
gravo-magneto instability. The mass of the star grows in large accretion
outbursts that may explain FU Orionis events. At late times there is not
sufficient mass in the disc for outbursts to occur but the dead zone becomes
even more prominent as the disc cools. Large inner dead zones in the later
stages of disc evolution may help to explain observations of transition discs
with an inner hole.
