  Aims: To understand stellar magnetism and to test the validity of the
Babcock-Leighton flux transport mean field dynamo models with stellar activity
observations Methods: 2-D mean field dynamo models at various rotation rates
are computed with the STELEM code to study the sensitivity of the activity
cycle period and butterfly diagram to parameter changes and are compared to
observational data. The novelty is that these 2-D mean field dynamo models
incorporate scaling laws deduced from 3-D hydrodynamical simulations for the
influence of rotation rate on the amplitude and profile of the meridional
circulation. These models make also use of observational scaling laws for the
variation of differential rotation with rotation rate. Results: We find that
Babcock-Leighton flux transport dynamo models are able to reproduce the change
in topology of the magnetic field (i.e. toward being more toroidal with
increasing rotation rate) but seem to have difficulty reproducing the cycle
period vs activity period correlation observed in solar-like stars if a
monolithic single cell meridional flow is assumed. It may however be possible
to recover the $P_{cyc}$ vs $P_{rot}$ relation with more complex meridional
flows, if the profile changes in a particular assumed manner with rotation
rate. Conclusions: The Babcock-Leighton flux transport dynamo model based on
single cell meridional circulation does not reproduce the $P_{cyc}$ vs
$P_{rot}$ relation unless the amplitude of the meridional circulation is
assumed to increase with rotation rate which seems to be in contradiction with
recent results obtained with 3-D global simulations.
