一维气候时间序列的拓展及其相空间中浑沌吸引子维数的确定

EXTENTION OF 1 - D CLIMATIC TIME - SERIES AND DETERMINATION OF DIMENSION OF CHAOTIC ATTRACTOR IN MUTIL- DIMENSIONAL PHASE SPACE

本文利用上海和广州近百年(1873—1980)月平均气温时间序列资料,将一维气候时间序列拓展到多维相空间上去。计算结果表明,月平均气温所表示的我国季风区短期气候演化,在相空间中存在吸引子,具有分维结构,其维数分别是d=3.4和d=2.3,为奇怪吸引子。由此推论,就我国季风区气候短期变化而言,为了能在多维相空间支撑起上述奇怪吸引子,最好选取四个变量或者建立最低为四阶的动力学模式来进行描述。

In this paper, monthly mean temperatures of 1873- 1980 for Shanghai and Guangzhou are used to extend the 1- D climatic time -series into a multi- dimensional phase space. Calculation results show that fractional dimensions attractors develop in the phase space in the short-range climate evolu -tion displayed by the monthly mean temperatures over the summer monsoon region in China. Their dimensions are d1=3.4 and d2=2.3 respectively.It is seen that the climate evolution would be best described by four variables or a dynamic model with no less than four steps, required by the development of these chaotic attractors in the multi - dimensional phase space.