黄河流域动力系统泥沙时序混沌特征分析——地理系统综合研究的一种尝试

选取黄河头道拐、潼关、花园口和利津断面1952²000年的泥沙含量为时序,在G-P重构相空间的基础上,分别计算了各断面泥沙时序的关联维（D2）、K2熵和Hurst指数。结果表明,各断面的最小饱和镶嵌维（m）、D2和K2熵分别为5、3.24和0.13,说明黄河流域各级系统均具有混沌特征,并且从上游到下游混沌特性逐渐增强。随着混沌特性的增强其平均可预报时间下降,头道拐断面为8年,其余断面为3年。各断面Hurst指数均大于0.68,在可预报时间内,各断面泥沙时序具有持续性下降趋势,并用2001²004年实际数据得到了验证。文章还给出了黄河流域动力系统的一般形式,该系统至少需要8个状态变量,2个控制变量。

Chaotic characters of dynamic system of the Yellow River basin from sandiness time series:an integrative research attempt to geographic system

The sandiness content on every section of the Yellow River relates all the factors that are interactive in many ways,so it includes some evolution information of the system controlled by monitoring section.We can infer the dynamic characters of the system from the sandiness time series based on the techniques of phase space reconstruction and the picking-up methods for chaos indexes.Sandiness contents from 1952 to 2000 were chosen as the time series on Toudaoguai section,Tongguan section,Huayuankou section and Lijin section along the Yellow River.Correlation dimension(D₂) was calculated according to Grassberger-Procaccia arithmetic,Kolmogorov entropy(K₂) according to Zhao Gui-bing arithmetic,and Hurst index（H） according to Rescaled Range Analysis（R/S）.The results are shown as follows:（1） The correlation dimension on Toudaoguai section is 3.24,Tongguan section is 5.69,Huayuankou section is 6.57 and Lijin section is 7.34.We can see that all the dimensions are fractal dimensions,so the dynamic systems controlled by different sections of the Yellow River basin are chaotic systems and the chaotic degrees heighten gradually from upper section to lower section.（2） Forecast time of the time series was calculated by 1/K₂.On Toudaoguai section,the forecast time of the sandiness time series is about 8 years,and the other sections are 3 years.The more obvious the chaos is,the shorter the forecast time is.（3） Hurst indexes on all the study sections are more than 0.5, the maximum is 0.86 on Tongguan section and the minimum is 0.68 on Toudaoguai section,which indicates that the changes of the time series have persistence trends in the average forecasting time.The past trends of the time series from 1952 to 2000 on all the sections were wavelike descending,so that the future trends of the time series will go on wavelike descending too.Compared with the time series from 1999 to 2000,the future trends was validated with the time series from 2001 to 2004 on Tongguan section,Huayuankou section and Lijin section.（4） We can get some information from correlation dimensions and saturated inlay dimensions to construct useful dynamic system model.The sandiness time series on Lijin section infers the dynamic characters of the whole Yellow River basin,its correlation dimension is 7.34 and the saturated inlay dimension is 10.Therefore,the dynamic model of the whole Yellow River basin needs eight state variables and two control variables at least.A general form of the dynamic model of the whole Yellow River basin was given in this paper.