  We consider dynamo action driven by three-dimensional rotating anelastic
convection in a spherical shell. Motivated by the behaviour of the solar
dynamo, we examine the interaction of hydromagnetic modes with different
symmetries and demonstrate how complicated interactions between convection,
differential rotation and magnetic fields may lead to modulation of the basic
cycle. For some parameters, Type 1 modulation occurs by the transfer of energy
between modes of different symmetries with little change in the overall
amplitude, for other parameters, the modulation is of Type 2, where the
amplitude is significantly affected (leading to grand minima in activity)
without significant changes in symmetry. Most importantly, we identify the
presence of "supermodulation" in the solutions, where the activity switches
chaotically between Type 1 and Type 2 modulation, this is believed to be an
important process in solar activity.
