  Recent data on superflares on sun-like stars and radiocarbon data on solar
activity in the past are both indicative of transient epochs of unusually high
magnetic activity. We propose an explanation for the grand activity maxima in
the framework of a solar dynamo model with fluctuating parameters. Solar-type
dynamos are oscillatory because of the combination of the solar-type
differential rotation with positive (in the Northern hemisphere) alpha-effect.
An artificial reversal of the sign in the alpha-effect changes the dynamo to a
steady regime with hundreds of times larger magnetic energy compared to the
amplitude of the cyclic dynamo. Sufficiently large and durable fluctuations
reversing the sign of the alpha-effect during the growth phase of a magnetic
cycle can, therefore, cause a transient change to a steady dynamo with
considerably increased magnetic energy. This qualitative scenario for grand
activity maxima is supported by computations of the dynamo model with a
fluctuating alpha-effect. The computed statistics of several thousand magnetic
cycles gives examples of cycles with very high magnetic energy. Our preliminary
estimations, however, suggest that the probability of solar superflares is
extremely low.
