Nonlinear Characteristic Analysis Of Solar Activity

Chaos and fractal generally exist in many natural and social phenomena, and are the important embranchment of the nonlinear science. Recently, chaos and fractal have been widely studied and applied in many areas with the improvement of the nonlinear theory, the advancement of the nonlinear analysis method and the fast development of the computer, such as biology, economics, physics and astronomy, of course including solar activity.Sunspot relative number shows the evolution characteristics of the solar longterm activity, plays an important role for describing the solar activity. On the basis of the sunspot relative number, it's shown that the Sun is governed by a low-dimensional chaotic attractor with the fractal structure and the solar activities display a north-south asymmetry. However, the sunspot generally emerges in the regions at the low latitude (±30°). Little has been known up to now about nonlinear characteristics of high-latitude solar activity. Firstly, the methods that recently were introduced to investigate the chaos and fractal of time series have been generalized. Then the nonlinear behaviour of the high-latitude solar activity has been studied, and the periodicity of high-latitude solar activity in the northern and southern hemispheres, respectively, and the phase relationship between two hemispheres also have been investigated using the new nonlinear methods. The results show that the high-latitude solar activity is also governed by a low-dimensional chaotic attractor, while the strength of chaotic behaviour between the northern and southern solar hemispheres is different. And it's concluded that the solar activity forecast can be predicted only for a short to medium term, but not for a long term. The high-latitude solar activity also have the Schwabe periodicity (11 year cycle) and possess the phase difference between the northern and southern hemispheres. The exact phase difference is obtained.Hoyt and Schatten (1998) constructed a new index, called as Group sunspot numbers. He selected the observing data to cover the gap in the sunspot relative numbers and improved the quality of the original data. Hence the level of noise in Group sunspot number is low than the relative sunspot numbers. Group sunspot number can more exactly and reliably describe the solar activity. On the basis of Group sunspot numbers, their nonlinear properties are investigated using the nonlinear analysis methods. It's found that the long-term dynamical behavior of Group sunspot numbers also is governed by a low-dimensional chaotic attractor. And the degree of chaotic behavior is almost consistent with the sunspot relative numbers. The chaotic attractor also shows that it's impossible to predict the long-term solar activity.In addition, the multifractality of the daily sunspot relative numbers (from maximum of 22 cycle to minimum 23 cycle) is studied to determine the complexity of solar activity by computing the multifractal spectrum. The data is divided into six sections for northern and southern hemispheres, respectively. The results display that the daily sunspot relative numbers have the multifractal structures. And the maximum, the minimum, the ascending section and the descending section of the cycle display the complexity of the different degree, namely the strength of the multifractality is anti-correlated with the counts of each section of the daily sunspot relative numbers, which is consistent with the prevenient study. The low fractal exponents are dominant in daily sunspot relative numbers. Thus, the small fluctuations are prevalent in the daily sunspot relative numbers.