【作者】 李启秀；

【导师】 李可军；

【作者基本信息】 中国科学院研究生院（云南天文台） ， 天体物理， 2008， 博士

【摘要】 混沌和分形普遍存在于很多自然和社会现象中,是非线性科学重要的两大分支学科。近年来,随着非线性理论的不断完善,非线性分析方法的不断提出和计算机技术的迅猛发展,混沌和分形在很多领域已经得到广泛地研究和应用,比如生物学,经济学,物理学和天文学等等,当然也包括太阳活动关于混沌和分形特征的研究。太阳黑子相对数表征着太阳长期演化活动的特征,在太阳活动描述中占有重要的地位。基于黑子相对数,已经证实太阳活动受控于一个低维的混沌吸引子,这个混沌吸引子还具有分形结构。太阳活动在南北半球上具有不对称性,这是近年来太阳物理研究的主要内容之一,基于黑子相对数,太阳活动南北半球不对称性也得到广泛的研究。然而,黑子一般出现在太阳球面的低纬度区域(±30°)。到目前为止,关于高纬度的太阳活动非线性特征的研究还很少。本文首先总结了近年来提出的研究混沌和分形的方法,然后主要研究了高纬度太阳活动的混沌行为,在此基础上,运用新的非线性方法,进一步研究了高纬度太阳活动在南北半球之间的周期性和相位关系。研究结果表明:高纬度太阳活动同样受控于一个低维的混沌吸引子,但是南北半球之间的混沌吸引子具有不同强度的混沌行为,同时还证明了高纬度太阳活动只能进行短期和中期的活动预报,不能进行长期的活动预报;高纬度的太阳活动也具有Schwabe周期(11年周期),南北半球之间的活动也具有相位差异,本文同时得到了具体的相位差。Hoyt和Schatten(1998)提出的群黑子数,成功地选择了被黑子相对数遗漏的观测,改善了原始数据的质量,噪音比黑子相对数的低,能更准确、更可靠地描述太阳活动,因此被认为是黑子相对数的一种取代。基于群黑子数,运用时间序列的非线性分析方法,我们研究了群黑子数的非线性动力学性质,发现群黑子数的长期动力学行为也表现为一个低维的混沌吸引子,且表现出来的混沌强度与黑子相对数的几乎一致。群黑子数的混沌吸引子也表明,长期太阳活动预报是不可能的。本文还采用计算多重分形谱的方法,分析了每日相对黑子数的多重分形特征以确定太阳活动的复杂性。结果发现每日相对黑子数具有多重分形性质,且在活动周的极大,极小,上升和下降阶段表现出不同程度的复杂性,多重分形的强度和每个阶段的每日黑子相对数的总数反相关,这与前人的研究结果一致。每日黑子相对数还展现出低分形指数占优势,因此在太阳黑子相对数中,小波动是占优势的。更多还原

【Abstract】 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.更多还原