Multi-fractal Property and Long-Range Correlation of Chaotic Time Series

The multi-fractal structure and long-range memory reveal the scale invariance of irregular objects in nature, and have been the subject of substantial interest due to the wide range of phenomena associated with many aspects, appearing in several scientific areas. Two quantitative analysis approaches, including multi-fractal analysis and rescaled range analysis, are combined to analyze the magnetic complexity and multi-fractal behavior of solar Ha flare activity. The following prominent results are found: (1) The calculated values of Hurst exponent for solar flare activity lie in between 0.8362 and 0.9420, exhibiting the persistent behavior of long-range correlation, (2) The values of fractal dimension reflect that solar flare activity in the northern hemisphere is more irregular than that in the southern hemisphere and in the whole solar disk, (3) The values of predictability indicator of solar flare activity are larger than 0.5, implying that solar flare activity is predictable and chaotic in nature, (4) The widths of singularity spectra indicate that solar flare activity has multi-fractal behavior and such multi-fractal nature is due to long-range correlation. These findings may be instructive to the physical processes of flare energy storage and dissipation, and to be useful for predicting solar flare eruption.