  The solar dynamo is essentially a cyclic process in which the toroidal
component of the magnetic field is converted into the poloidal one and vice
versa. This cyclic loop is disturbed by some nonlinear and stochastic processes
mainly operating in the toroidal to poloidal part. Hence, the memory of the
polar field decreases in every cycle. On the other hand, the dynamo efficiency
and, thus, the supercriticality of the dynamo decreases with the Sun's age.
Previous studies have shown that the memory of the polar magnetic field
decreases with the increase of supercriticality of the dynamo. In this study,
we employ popular techniques of time series analysis, namely, compute Higuchi's
fractal dimension, Hurst exponent, and Multi-Fractal Detrended Fluctuation
Analysis, to the amplitude of the solar magnetic cycle obtained from dynamo
models operating at near-critical and supercritical regimes. We show that the
magnetic field in the near-critical regime is governed by strong memory, less
stochasticity, intermittency, and breakdown of self-similarity. On the
contrary, the magnetic field in the supercritical region has less memory,
strong stochasticity, and shows a good amount of self-similarity. Finally,
applying the same time series analysis techniques in the reconstructed sunspot
data of 85 cycles and comparing their results with that from models, we
conclude that the solar dynamo is possibly operating near the critical regime
and not too much supercritical regime. Thus Sun may not be too far from the
critical dynamo transition.
