  The Babcock-Leighton (BL) flux-transport model is a widely-accepted dynamo
model of the Sun. This dynamo model has been extensively studied in a
two-dimensional (2D) mean-field framework in both kinematic and non-kinematic
regimes. Recent three-dimensional (3D) models have been restricted to the
kinematic regime. In these models, the surface poloidal flux is produced by the
emergence of bipolar magnetic regions (BMRs) that are tilted according to Joy's
law. We investigate the prescription for emergence of a BMR in 3D non-kinematic
simulations. We also report initial results of cyclic BL dynamo simulation. We
extend a conventional 2D mean-field model of the BL flux-transport dynamo into
3D non-kinematic regime. The large-scale mean flows are driven by the
parameterized $\Lambda$-effect in this model. For the induction equation, we
use a BL source term by which the surface BMRs are produced in response to the
dynamo-generated toroidal field inside the convection zone. We find that, in
the 3D non-kinematic regime, the tilt angle of a newly-emerged BMR is very
sensitive to the prescription for the subsurface structure of the BMR. Anti-Joy
tilt angles are found unless the BMR is deeply embedded in the convection zone.
We also find that the leading spot tends to become stronger than the following
spot. The anti-Joy's law trend and the morphological asymmetry of the BMRs can
be explained by the Coriolis force acting on the Lorentz-force-driven flows.
Furthermore, we demonstrate that the solar-like magnetic cycles can be
successfully obtained if the Joy's law is explicitly given in the BL
$\alpha$-effect. In these cyclic dynamo simulation, a strong Lorentz force
feedback leads to cycle modulations in the differential rotation and meridional
circulation. The non-axisymmetric components of the flows are found to exist as
inertial modes such as the equatorial Rossby modes.
