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In Sun and sun-like stars, it is believed that the cycles of the large-scalemagnetic field are produced due to the existence of differential rotation andhelicity in the plasma flows in their convection zones (CZs). Hence, it isexpected that for each star, there is a critical dynamo number for theoperation of a large-scale dynamo. As a star slows down, it is expected thatthe large-scale dynamo ceases to operate above a critical rotation period. Inour study, we explore the possibility of the operation of the dynamo in thesubcritical region using the Babcock--Leighton type kinematic dynamo model. Insome parameter regimes, we find that the dynamo shows hysteresis behavior,i.e., two dynamo solutions are possible depending on the initial parameters --decaying solution if started with weak field and strong oscillatory solution(subcritical dynamo) when started with a strong field. However, under largefluctuations in the dynamo parameter, the subcritical dynamo mode is unstablein some parameter regimes. Therefore, our study supports the possible existenceof subcritical dynamo in some stars which was previously shown in a mean-fielddynamo model with distributed $\alpha$ and MHD turbulent dynamo simulations.

Subcritical dynamo and hysteresis in a Babcock-Leighton type kinematic dynamo model