Abstract
A solar-type dynamo model in a spherical shell is developed with allowance for random dependence of the poloidal field generation mechanism on time and latitude. The model shows repeatable epochs of strongly decreased amplitude of magnetic cycles similar to the Maunder minimum of solar activity. Random dependence of dynamo-parameters on latitude brakes the equatorial symmetry of generated fields. The model shows the correlation of the occurrence of grand minima with deviations in the dynamo-field from dipolar parity. An increased north-south asymmetry of magnetic activity can, therefore, be an indicator of transitions to grand minima. Qualitative interpretation of this correlation is suggested. Statistics of grand minima in the model are close to the Poisson random process indicating that the onset of a grand minimum is statistically independent of preceding minima.
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