淮河流域洪涝变化吸引子维数研究

STUDY ON THE ATTRACTOR DIMENSION OF THE FLOOD SERIES IN HUAIHE RIVER BASIN

淮河流域洪涝序列的功率谱表现出了较好的混沌谱特征，这是序列呈分形结构的内在原因。洪涝序列及其不同平滑序列的关联维数表明，序列平滑程度越大，关联维数越小。关联维数反映了序列所在系统的层次，是系统结构复杂性的重要量度，是系统建模所需独立变量的控制参数。要恰当地描述淮河流域洪涝发生系统，需构造至少５个状态变量的动力学系统。

Mang researches have been made about the flood series based on the abundant historical data in the Huaihe River basin, like other basins in China. The work mainly focused on the history data's arrangement, reconstruction and statistical analysis, like periodic analysis. The inherent nonlinear trait of the series studied less. In recent years, the nonlinear applied researches in earth sciences are being paid attention with the development of the nonlinear sciences, such as fractals, chaotic theory. The flood series in the Huaihe River basin is a kind of an irregular Contor Set that is a typical fractal structure. The power spectral feature which is similar to the characteristic of a chaotic series spectrum means that the flood series in the Huaihe River basin is a chaotic series. In chaotic theory, attracttor dimension is an important parameter. It cab be represented by correlative dimension. The correlative dimensions of the flood series and some time moving series in the Huiahe River basin are studied according to the theorem of embedding phace. The results show that the correlative dimension reflects the systematic hierarchy. The smaller the fractal dimension, the more obvious the tendency of the system, and vice versa. The correlative dimension is an important judgment to the complexity of a system. Reconstructing a dynamic system should have at least 5 independent parameters according to the attractor dimension (4.66) of the flood series. This is practical to the simulation or reconstruction of the flood series.