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We explore a reduced Babcock-Leighton (BL) dynamo model based on delaydifferential equations using numerical bifurcation analysis. This model revealshysteresis, seen in the recent mean-field dynamo model and the direct numericalsimulations of turbulent dynamos. The BL model with 'magnetic noise' as anadditional weak-source of the poloidal field recovers the solar cycle everytime from grand minima, which BL source alone cannot do. The noise-incorporatedmodel exhibits a bimodal distribution of toroidal field energy confirming twomodes of solar activity. It also shows intermittency and reproduces phase spacecollapse, an experimental signature of the Maunder Minimum. The occurrencestatistics of grand minima in our model agree reasonably well with the observedstatistics in the reconstructed sunspot number. Finally, we demonstrate thatthe level of magnetic noise controls the duration of grand minima and even hasa handle over its waiting period, suggesting a triggering effect of grandminima by the noise and thus shutting down the global dynamo. Therefore, weconclude that the 'magnetic noise' due to small-scale turbulent dynamo action(or other sources) plays a vital role even in Babcock-Leighton dynamo models.

Origin and Recovery from Grand Solar Minima in a Time Delay Dynamo Model with Magnetic Noise as an Additional Poloidal Source