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Solar cycles vary in their amplitude and shape. There are several empiricalrelations between various parameters linking cycle's shape and amplitude, inparticular the Waldmeier relations. As solar cycle is believed to be a resultof the solar dynamo action, these relations require explanation in theframework of this theory.Here we aim to present a possible explanation of suchkind. We relate the cycle-to-cycle variability of solar activity tofluctuations of solar dynamo drivers and primarily to fluctuations in theparameter responsible for recovery of the poloidal magnetic field from thetoroidal one. To be specific, we develop such a model in the framework of themean-field dynamo based on the differential rotation and $\alpha$-effect. Wedemonstrate that the mean-field dynamo based on a realistic rotation curve andnonlinearity associated with the magnetic helicity balance reproduces bothqualitatively and quantitatively the Waldmeier relations observed in sunspotdata since 1750 (SIDC data). The model also reproduces more or lesssuccessfully other relations between the parameters under discussion, inparticular, the link between odd and even cycles (Gnevyshev-Ohl rule). Weconclude that the contemporary solar dynamo theory provides a way to explainthe cycle-to-cycle variability of solar activity as recorded in sunspots. Wediscuss the importance of the model for stellar activity cycles which, as knownfrom the data of HK project, demonstrate the cycle-to-cycle variability similarto solar cycles.

Variations of the solar cycle profile in a solar dynamo with fluctuating dynamo governing parameters