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

点击翻译按钮获取中文摘要

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.