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Development of a system for the time series analysis of paleoenvironment by the embeddeing dimension method

嵌入维数法古环境时间序列分析系统的开发

基本信息

批准号：
62840025
负责人：
ITO Keisuke
金额：
$ 3.71万
依托单位：
Kobe University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Developmental Scientific Research
财政年份：
1987
资助国家：
日本
起止时间：
1987 至 1988
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-62840025/
关键词：
Chaos Fractal dimension Embedding Time-series analysis sun-spots 気候変動

项目摘要

1. Construction of the system for analysis. A workstation with a plenty of memory is the center of the system. A couple of personal computers are connected with it through the high-speed ethernet and used as terminals. Development of programs, input of large amounts of data, time-sharing of jobs, and graphic output are performed efficiently as well as easily. 2. Programs for analysis. The optimum time delay for embedding is estimated on the basis of autocorrelation. mutual information, and poincare section. The best time delay is selected that gives the widest scaling region. Then, we compute the point-wise dimension from randomly chosen reference points. Only good reference points are selected that give clear scaling region. Using selected reference points, correlation and information dimensions of attractor is finally obtained after averaging process. 3. Applications of the results. When the attractor dimension is obtained, local deterministic vectors are computed on a phase space with the obtained degree of freedom. local vectors are used as predictors. 4. The variation of sunspot numbers. The sunspot numbers are analysed by the above-mentioned method. We find that the variation has a low-dimensional attractor with the fractal dimension of 4.2. This implies that the dynamics generating sunspot numbers can be described by a set of deterministic equation with only 5 variables. We are trying to find if paleoclimate has a small degree of freedom. If so, then results can be used for insertion and prediction.

1. 对系统的构建进行了分析。拥有大量内存的工作站是系统的中心。两台个人电脑通过高速以太网与之连接，作为终端使用。程序的开发、大量数据的输入、作业的分时分配和图形输出都可以高效而轻松地完成。2. 用于分析的程序。在自相关的基础上估计了最优的嵌入时延。互信息，和庞加莱节。选择给出最宽缩放区域的最佳延时。然后，我们从随机选择的参考点计算逐点维数。只有选择好的参考点，给出明确的缩放区域。选取参考点，经过平均处理，最终得到吸引子的相关维数和信息维数。3. 结果的应用。当获得吸引子维数后，在获得自由度的相空间上计算局部确定性向量。局部向量被用作预测因子。4. 太阳黑子数的变化。用上述方法对太阳黑子数进行了分析。我们发现变异具有低维吸引子，分形维数为4.2。这意味着产生太阳黑子数的动力学可以用一组只有5个变量的确定性方程来描述。我们试图发现古气候是否有一定程度的自由。如果是这样，那么结果可以用于插入和预测。