  Fluctuations in the Sun's magnetic activity, including episodes of grand
minima such as the Maunder minimum have important consequences for space and
planetary environments. However, the underlying dynamics of such extreme
fluctuations remain ill-understood. Here we use a novel mathematical model
based on stochastically forced, non-linear delay differential equations to
study solar cycle fluctuations, in which, time delays capture the physics of
magnetic flux transport between spatially segregated dynamo source regions in
the solar interior. Using this model we explicitly demonstrate that the
Babcock-Leighton poloidal field source based on dispersal of tilted bipolar
sunspot flux, alone, can not recover the sunspot cycle from a grand minimum. We
find that an additional poloidal field source effective on weak fields--the
mean-field alpha-effect driven by helical turbulence--is necessary for
self-consistent recovery of the sunspot cycle from grand minima episodes.
