Chaotic characters of dynamic system of the Yellow River basin from sandiness time series:an integrative research attempt to geographic system
Received date: 2006-05-08
Revised date: 2006-09-20
Online published: 2006-12-15
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.
MA Jian-hua,CHU Chun-jie . Chaotic characters of dynamic system of the Yellow River basin from sandiness time series:an integrative research attempt to geographic system[J]. GEOGRAPHICAL RESEARCH, 2006 , 25(6) : 949 -958 . DOI: 10.11821/yj2006060001
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