• 论文 •

### 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

1. 1. 河南大学资源与环境研究所,开封475004;
2. 平顶山学院环境与地理科学系,河南平顶山467000
• 收稿日期:2006-05-08 修回日期:2006-09-20 出版日期:2006-12-15 发布日期:2006-12-15
• 作者简介:马建华(1958-),男,河南省清丰人,教授,博士生导师。主要从事自然地理学和环境科学研究,已 发表论文50余篇,出版著作和教材10部。E-mail:mjh@henu.edu.cn
• 基金资助:

国家自然科学基金资助项目(30570301)

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

MA Jian-hua1, CHU Chun-jie2

1. 1. Institute of Natural Resources and Environmental Science,Henan University,Kaifeng 475001,China;
2. Department of Environment and Geography,Pingdingshan Henan,467000,China
• Received:2006-05-08 Revised:2006-09-20 Online:2006-12-15 Published:2006-12-15

Abstract:

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.