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

Research Project

Project/Area Number	62840025
Research Category	Grant-in-Aid for Developmental Scientific Research
Allocation Type	Single-year Grants
Research Field	Stratigraphy/Paleontology
Research Institution	Kobe University
Principal Investigator	ITO Keisuke Faculty of Science, Kobe University, Professor, 理学部, 教授 (00030792)
Co-Investigator(Kenkyū-buntansha)	KOIZUMI Itaru Colledge of General Education, Osaka University, Associate Professor, 教養部, 助教授 (20029721) GUNJI Yukio Faculty of Science, Kobe University, Research Associate, 理学部, 助手 (40192570)
Project Period (FY)	1987 – 1988
Project Status	Completed (Fiscal Year 1988)
Budget Amount *help	¥5,800,000 (Direct Cost: ¥5,800,000) Fiscal Year 1988: ¥500,000 (Direct Cost: ¥500,000) Fiscal Year 1987: ¥5,300,000 (Direct Cost: ¥5,300,000)
Keywords	Chaos / Fractal dimension / Embedding / Time-series analysis / sun-spots / 気候変動
Research Abstract	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.