feedback on the differential rotation, see details in the Table 2. The realistic model should include all those effects into account. [The output of the models which we will use for comparison with observations includes, the total magnetic flux, which is integrated unsigned magnetic flux of the toroidal field over the bulk of the convection zone, the period of the magnetic cycle, the total Poynting flux from subsurface shear layer.]{}

Spatial structure of dynamo waves
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Figure 1 shows the time-latitude diagrams for the radial magnetic field at the surface and the near-surface toroidal magnetic field for the model D0, which takes into account the nonlinear $\alpha$- effect, and the magnetic buoyancy for the rotation periods of 25 and 15 days. Figure 2 shows the same as Figure 1 for the model B0. The butterfly diagrams of the model B0 for the period of rotation 25 days is rather similar to those by @2011AstL...37..286K. [They noticed that in the model with the non-local $\alpha$-effect the dynamo wave does not follow to the Parker-Yoshimura rule. Thus, in their model the equatorward propagation of the dynamo wave is likely due to the joint action of the latitudinal shear and the strong diamagnetic 