李建平,丑纪范. 1996. 利用一维时间序列确定吸引子维数中存在的若干问题[J]. 气象学报, 54(3):312-323, doi:10.11676/qxxb1996.032
利用一维时间序列确定吸引子维数中存在的若干问题
SOME PROBLEMS EXITED IN ESTIMATING FRACTAL DIMENSION OF ATTRACTOR WITH ONEDIMENSIONAL TIME SERIES
投稿时间:1994-10-17  修订日期:1995-05-22
DOI:10.11676/qxxb1996.032
中文关键词:  分维  一维时间序列  动力系统  相空间  重构相空间  吸引子
英文关键词:Fractal dimension  One-dimension time series  Dynamic system  Original phase-space. Reconstructed phase-space  Attractor
基金项目:国家基础性重大关键项目“气候动力学和气候预测的研究”资助
作者单位
李建平 兰州大学大气科学系, 兰州, 730000 
丑纪范 兰州大学大气科学系, 兰州, 730000 
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中文摘要:
      从一些控制方程已知的微分动力系统出发,利用它们不同分量、不同时间间隔的解序列重构相空间和原本相空间两种方式所得分维结果进行了比较,发现了一些有意义的事实,并探讨了用一维时间序列重构相空间确定吸引子维数的理论,揭示出其中存在的本质问题。最后指出,只有完全搞清动力系统的单分量序列采用怎样的延滞时间τ和怎样的采样间隔H延拓后才能保证重构相空间和原本相空间的度量性质不变时,我们才能获得真实、可靠、有用的结果。
英文摘要:
      Based on the some differential dynamic systems of known control equations, it is found that there existed some essential problems in estimating the fractal dimensions of attractors with one dimensional time series. by a comparison between the two fractal dimension results of the reconstructed phase-space,which is made according to their solution series of different components and different time intervals, and of the original phase-space. Some significant facts are found. Then, the theory of reconstructed phase-space with one dimensional time series is discussed and some essential problems exited in it are found. Finally, it should be pointed out that the real, reliable, useful resuits would be obtained only when the clear understanding of what kind of the delay time r and the sample interval H are used in a single-variable of the dynamic system to keep the same measure nature between the reconstructed phase-space and the original phase-space.
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