  The polar magnetic field precursor is considered to be the most robust and
physics-based method for the prediction of the next solar cycle strength.
However, to make a reliable prediction of a cycle, is the polar field at the
solar minimum of the previous cycle enough or we need the polar field of many
previous cycles? To answer this question, we performed several simulations
using Babcock-Leighton type flux transport dynamo models with the
stochastically forced source for the poloidal field ($\alpha$ term). We show
that when the dynamo is operating near the critical dynamo transition or only
weakly supercritical, the polar field of the cycle n determines the amplitude
of the next several cycles (at least three). However, when the dynamo is
substantially supercritical, this correlation of the polar field is reduced to
one cycle. This change in the memory of the polar field from multi- to
one-cycle with the increase of the super-criticality of the dynamo is
independent of the importance of various turbulent transport processes in the
model. We further show that when the dynamo operates near the critical, it
produces frequent extended episodes of weaker activity, resembling the solar
grand minima. The occurrence of grand minima is accompanied by the multi-cycle
correlation of polar field. The frequency of grand minima decreases with the
increase of supercriticality of the dynamo.
