  We propose that grand minima in solar activity are caused by simultaneous
fluctuations in the meridional circulation and the Babcock-Leighton mechanism
for the poloidal field generation in the flux transport dynamo model. We
present the following results: (a) fluctuations in the meridional circulation
are more effective in producing grand minima; (b) both sudden and gradual
initiations of grand minima are possible; (c) distributions of durations and
waiting times between grand minima seem to be exponential; (d) the coherence
time of the meridional circulation has an effect on the number and the average
duration of grand minima, a coherence time of about 30 years being consistent
with observational data. We also study the occurrence of grand maxima and find
that the distributions of durations and waiting times between grand maxima are
also exponential, like the grand minima. Finally we address the question
whether the Babcock-Leighton mechanism can be operative during grand minima
when there are no sunspots. We show that an alpha-effect restricted to the
upper portions of the convection zone can pull the dynamo out of the grand
minima and can match various observational requirements if the amplitude of
this alpha-effect is suitably fine-tuned.
