  We aim to investigate the nature and occurrence characteristics of grand
solar minimum and maximum periods, which are observed in the solar proxy
records such as 10Be and 14C, using a fully non-linear Babcock-Leighton type
flux-transport dynamo including momentum and entropy equations. The
differential rotation and meridional circulation are generated from the effect
of turbulent Reynolds stress and are subjected to back-reaction from the
magnetic field. To generate grand minimum and maximum-like periods in our
simulations, we used random fluctuations in the angular momentum transport
process, namely the Lambda-mechanism, and in the Babcock-Leighton mechanism. To
characterise the nature and occurrences of the identified grand minima and
maxima in our simulations, we used the waiting time distribution analyses,
which reflects whether the underlying distribution arises from a random or a
memory-bearing process. The results show that, in majority of the cases, the
distributions of grand minima and maxima reveal that the nature of these events
originates from memoryless processes. We also found that in our simulations the
meridional circulation speed tends to be smaller during grand maximum, while it
is faster during grand minimum periods. The radial differential rotation tend
to be larger during grand maxima, while it is smaller during grand minima. The
latitudinal differential rotation on the other hand is found to be larger
during grand minima.
