Low-dimensional chaos and fractal properties of long-term sunspot activity

Two primary solar-activity indicators− sunspot numbers (SNs) and sunspot areas (SAs) in the time interval from November 1874 to December 2012 − are used to determine the chaotic and fractal properties of solar activity. The results show that (1) the long-term solar activity is governed by a low-dimensional chaotic strange attractor, and its fractal motion shows a long-term persistence on large scales; (2) both the fractal dimension and maximal Lyapunov exponent of SAs are larger than those of Sns, implying that the dynamical system of SAs is more chaotic and complex than SNs; (3) the predictions of solar activity should only be done for short- to mid-term behaviors due to its intrinsic complexity; moreover, the predictability time of SAs is obviously smaller than that of SNs and previous results.

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