  The Sun and solar-type stars exhibit irregular cyclic variations in their
magnetic activity over long time scales. To understand this irregularity, we
employed the flux transport dynamo models to investigate the behavior of one
solar mass star at various rotation rates. To achieve this, we have utilized a
mean-field hydrodynamic model to specify differential rotation and meridional
circulation, and we have incorporated stochastic fluctuations in the
Babcock-Leighton source of the poloidal field to capture inherent fluctuations
in the stellar convection. Our simulations successfully demonstrated
consistency with the observational data, revealing that rapidly rotating stars
exhibit highly irregular cycles with strong magnetic fields and no Maunder-like
grand minima. On the other hand, slow rotators produce smoother cycles with
weaker magnetic fields, long-term amplitude modulation, and occasional extended
grand minima. We observed that the frequency and duration of grand minima
increase with the decreasing rotation rate. These results can be understood as
the tendency of a less supercritical dynamo in slow rotators to be more prone
to produce extended grand minima. We further explore the possible existence of
the dynamo in the subcritical regime in a Babcock-Leighton-type framework and
in the presence of a small-scale dynamo.
