goal of this paper is to examine this relation for a range of the rotation rates faster than the solar rotation.

The study explores the rotational periods from 15 to 30 days. We assume that the initial structure of the differential rotation corresponds to the current results from helioseismology [@Howe2011JPh]. Results of @2014ApJ...791...59K confirm this assumption, which is also supported by observations [@2011IAUS_saar]. The paper studies a set of nonlinear dynamo models which take into account the magnetic feedback on the angular momentum balance, the magnetic helicity conservation and the magnetic buoyancy effect. Two type of the dynamo models will be discussed: 1) the D-type model, with the $\alpha$-effect in the bulk of the convection zone; 2) the B-type model with the non-local $\alpha$- effect. Confronting two approaches allows us to explore how distribution of the turbulent sources of the dynamo impact the properties of the magnetic cycles. Also, it is interesting to confront the nonlinear saturation in the different types of the mean-field dynamos. Our results are preliminary because the meridional circulation is not included in the study.

Basic equations
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Dynamo model\[DM\]
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Following @KR80, we explore the evolution of the induction vector of the mean field, $\overline{\mathbf{B}}$, 