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

1.对系统的构建进行分析。一个具有大量内存的工作站是系统的中心。几台个人计算机通过高速以太网与它相连，用作终端。程序的开发、大量数据的输入、作业的分时以及图形输出都可以高效且容易地进行。2.分析程序。嵌入的最佳时间延迟估计的自相关的基础上。相互信息和庞加莱分部选择给出最宽缩放区域的最佳时间延迟。然后，我们从随机选择的参考点计算逐点维数。仅选择给出清晰缩放区域的良好参考点。利用选取的参考点，经过平均处理，最终得到吸引子的关联维数和信息维数。3.结果的应用。当获得吸引子维数时，在具有所获得的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器。4.太阳黑子数量的变化。用上述方法分析了太阳黑子数。我们发现，变化有一个低维吸引子的分形维数为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个小的自由度。如果是，则结果可以用于插入和预测。

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.