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Over the course of their lifetimes, the rotation of solar-type stars goesthrough different phases. Once they reach the zero-age main sequence, theirglobal rotation rate decreases during the main sequence until at least thesolar age, approximately following the empirical Skumanich's law and enablinggyrochronology. Older solar-type stars might then reach a point of transitionwhen they stop braking, according to recent results of asteroseismology.Additionally, recent 3D numerical simulations of solar-type stars show thatdifferent regimes of differential rotation can be characterized with the Rossbynumber. In particular, anti-solar differential rotation (fast poles, slowequator) may exist for high Rossby number (slow rotators). If this regimeoccurs during the main sequence and, in general, for slow rotators, we mayconsider how magnetic generation through the dynamo process might be impacted.In particular, we consider whether slowly rotating stars are indeed subject tomagnetic cycles.  We find that kinematic $\alpha$ $\Omega$ dynamos allow for the presence ofmagnetic cycles and global polarity reversals for both rotation regimes, butonly if the $\alpha$-effect is saddled on the tachocline. If it is distributedin the convection zone, solar-type cases still possess a cycle and anti-solarcases do not. Conversely, we have not found any possibility for sustaining amagnetic cycle with the traditional Babcock-Leighton flux-transport dynamos inthe anti-solar differential rotation regime due to flux addition. Graphicinterpretations are proposed in order to illustrate these cases. However, wefind that hybrid models containing both prescriptions can still sustain localpolarity reversals at some latitudes.  We conclude that stars in the anti-solar differential rotation regime cansustain magnetic cycles only for very specific dynamo processes.

Impact of anti-solar differential rotation in mean-field solar-type dynamos -- Exploring possible magnetic cycles in slowly rotating stars