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Nonlinear mean-field models of the solar dynamo show long-term variability,which may be relevant to different states of activity inferred from long-termradiocarbon data. This paper is aimed to probe the dynamo hysteresis predictedby the recent mean-field models of Kitchatinov \& Olemskoy (2010) with directnumerical simulations. We perform three-dimensional simulations of large-scaledynamos in a shearing box with helically forced turbulence. As initialcondition, we either take a weak random magnetic field or we start from asnapshot of an earlier simulation. Two quasi-stable states are found to coexistin a certain range of parameters close to the onset of the large-scale dynamo.The simulations converge to one of these states depending on the initialconditions. When either the fractional helicity or the magnetic Prandtl numberis increased between successive runs above the critical value for onset of thedynamo, the field strength jumps to a finite value. However, when thefractional helicity or the magnetic Prandtl number is then decreased again, thefield strength stays at a similar value (strong field branch) even below theoriginal onset. We also observe intermittent decaying phases away from thestrong field branch close to the point where large-scale dynamo action is justpossible. The dynamo hysteresis seen previously in mean-field models is thusreproduced by 3D simulations. Its possible relation to distinct modes of solaractivity such as grand minima is discussed.

Hysteresis between distinct modes of turbulent dynamos