Parameters of magnetic activity on the solar type stars depend on the properties of the dynamo processes operating in stellar convection zones. We apply nonlinear mean-field axisymmetric $alpha^2Omega$ dynamo models to calculate of the magnetic cycle parameters, such as the dynamo cycle period, the total magnetic flux and the Poynting magnetic energy flux on the surface of solar analogs with the rotation periods from 15 to 30 days. The models take into account the principal nonlinear mechanisms of the large-scale dynamo, such as the magnetic helicity conservation, magnetic buoyancy, and effects of magnetic forces on the angular momentum balance inside the convection zones. Also, we consider two types of the dynamo models. The distributed (D-type) models employ the standard alpha-effect distributed on the whole convection zone. The boundary (B-type) models employ the non-local alpha- effect, which is confined to the boundaries of the convection zone. Both the D- and B-type models show that the dynamo-generated magnetic flux increases with the increase of the stellar rotation rate. {It is found that for the considered range of the rotational periods} the magnetic helicity conservation is the most significant effect for the nonlinear quenching of the dynamo. This quenching is more efficient in the B-type than in the D-type dynamo models. The D-type dynamo reproduces the observed dependence of the cycle period on the rotation rate for the Sun analogs. For the solar analog rotating with a period of 15 days we find nonlinear dynamo regimes with multiply cycles.
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