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The polar magnetic field precursor is considered to be the most robust andphysics-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 thesolar minimum of the previous cycle enough or we need the polar field of manyprevious cycles? To answer this question, we performed several simulationsusing Babcock-Leighton type flux transport dynamo models with thestochastically forced source for the poloidal field ($\alpha$ term). We showthat when the dynamo is operating near the critical dynamo transition or onlyweakly supercritical, the polar field of the cycle n determines the amplitudeof the next several cycles (at least three). However, when the dynamo issubstantially supercritical, this correlation of the polar field is reduced toone cycle. This change in the memory of the polar field from multi- toone-cycle with the increase of the super-criticality of the dynamo isindependent of the importance of various turbulent transport processes in themodel. We further show that when the dynamo operates near the critical, itproduces frequent extended episodes of weaker activity, resembling the solargrand minima. The occurrence of grand minima is accompanied by the multi-cyclecorrelation of polar field. The frequency of grand minima decreases with theincrease of supercriticality of the dynamo.

Supercriticality of the dynamo limits the memory of the polar field to one cycle