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.