Abstract
Solar magnetic activity exhibits a complex nonlinear behavior, but its dynamic process has not been fully understood. As the complex network technique can better capture the dynamics of nonlinear system, the visibility graphs (VG), the horizontal visibility graphs (HVG), and the limited penetrable visibility graphs (LPVG) are applied to implement the mapping of sunspot relative numbers in the northern and southern hemispheres. The results show that these three methods can capture important information of nonlinear dynamics existing in the long-term hemispheric sunspot activity. In the presentation of the results, the network degree sequence of the HVG method changes preferentially to the original data series as well as the VG and the LPVG, while both the VG and the LPVG slightly lag behind the original time series, which provides some new ideas for the nonlinear dynamics of the hemispheric asymmetry in the two hemispheres. Meanwhile, the use of statistical feature-skewness values and complex network visibility graphs can yield some complementary information for mutual verification.
Highlights
The complexity of solar magnetic activity and its long-term variability have been studied for a long time, and it was known as early as the last century that solar activity is characterized by the hemispheric asymmetry [1,2]
The longest record of solar activity variability is the number of sunspots, and the study of hemispheric asymmetry in the two hemispheres has gradually moved from sunspots to almost all solar activity phenomena, such as coronal mass ejections [4], flare activity [5,6,7], differential rotation [8,9], polar faculae [10,11], and so on
The transition period is consistent with the visibility graphs (VG) algorithm, and it is worth noting that the limited penetrable visibility graphs (LPVG) plays a certain effect of homogenizing the fluctuations of the transition period between the northern and southern hemispheres
Summary
The complexity of solar magnetic activity and its long-term variability have been studied for a long time, and it was known as early as the last century that solar activity is characterized by the hemispheric asymmetry [1,2]. By using the cross-correlation analysis, the cross wavelet transform, and the cross-recurrence plot methods, the temporal evolution of group sunspot numbers is found to be different between the two hemispheres, providing a lot of reference value for studying sunspot activity [22] These methods have advantages, considering the nonlinear dynamics of solar activity [23], the traditional linear methods have some limitations in predicting the solar cycle, which are not sufficient to fully capture the nonlinear dynamics of solar activity. Complex network-based visibility methods, including the visibility graphs (VG; [25]), the horizontal visibility graphs (HVG; [26]), and the limited penetrable visibility graphs (LPVG; [27]), have been applied with better feedback on processing nonlinear time series These methods showed that the improved visibility-based techniques have obtained better results in the solar physics field [28,29], which are more able to extract amplitude differences and phase differences of nonlinear systems.
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