Dynamo hysteresis and grand minima of solar activity

A nonlinear dynamo model that allows for the dependence of the turbulent diffusivity on the magnetic field shows the phenomenon of a hysteresis. In a certain range of dynamo numbers, two types of solutions are possible: decaying oscillations of weak fields and magnetic cycles with a constant and large amplitude, which are settled depending on the initial conditions. Fluctuations in alpha-parameter cause transitions between these two regimes and calculations show the intermittency of magnetic cycles with a relatively large amplitude and epochs of weak magnetic fields. This behavior can serve as a model of grand minima of solar activity like the well-known Maunder minimum.