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The solar magnetic activity is produced by a complex dynamo mechanism and exhibits nonlinear dissipation behavior in nature. The chaotic and fractal properties of solar activity phenomena are of great importance for understanding the nonlinear dynamo actions, especially nonlinear dynamo models. To study the chaotic and fractal properties of solar activity phenomena at the high-and low-latitudes, the polar faculae and sunspot numbers in the time interval from 1952 February to 1998 June are used to investigate their nonlinear dynamical behavior by the recurrence analysis method and Grassberger-Procaccia (G-P) algorithm. Firstly, the monthly average value of both polar faculae and sunspot numbers are smoothed to filter the noisy signal by the 13-point smoothing method. This procedure can keep the original dynamical information. Secondly, the correlation coefficient of these two solar activity indicators is analyzed, and the analysis results indicate that there is a negative correlation between polar faculae and sunspot numbers. To obtain more accurate results, the recurrence quantification analysis (RQA) is used to obtain the average value of the rate of DET by selecting four groups of different parameters. And then, we use the G-P algorithm to draw the correlation integral curve graphs and to obtain the correlation dimension of polar faculae and the sunspot numbers. Finally, the analysis results given by RQA and G-P algorithm are analyzed and compared by advanced statistical method. The main conclusions of this paper are as follows. 1) From a statistical point of view, the chaotic and fractal properties of high-and low-latitudes solar activity are different between in the northern hemisphere and in the southern hemisphere, owing to the fact that the temporal variation of solar activity is closely related to the magnetic field evolution. This result is in agreement with the previous results given by the polar faculae. It should be pointed out that this result is not the main goal of this article, we only reinforce this conclusion by the recurrence analysis and G-P algorithm. 2) The chaotic behaviors of solar magnetic activity at high latitude are stronger than at low latitude. Furthermore, the high-latitude solar activity in the northern hemisphere has the most complex fractal structure. Based on the solar nonlinear dynamo theory, the polar magnetic fields are the seed fields of the solar activity. That is to say, the physical meaning of polar faculae is more important than sunspot numbers. We think that our results are useful for understanding the physical nature of the systematic regularity of solar activity phenomena.

Chaos and fractal properties of solar activity phenomena at the high and low latitudes