摘要
本文采用上海(1970—1985年)15年逐日平均气压资料,用相关矩阵分析的方法,提取得到了完整的Lyapunov指数谱。指数谱不仅有正值、零值,还得到了负值。并得到Lyapunov指数之和,即∑λ_i<0。又一次证明了我国季风区短期天气吸引子是一种混沌运动。由于正的Lyapunov指数值之和是反映系统总体的发散状况,理论证明正值指数和等于系统的Kolmogorov熵。本文得到在延滞时间τ=5、参数m=2、维数d_M=9的条件下,正指数之和∑λ_i=K=0.110405从而得到可预报时间尺度T=1/K≈9天。与早期动力统计方法所得到的可预报时间接近,亦与作者在文献[2]中得到的结果十分吻合。
A complet Lyapunov index spectrum is extracted by using the Shanghai day-to-day mean pressure data of 15 years (1970-1985) and the correlation matrix analy-sis. The spectrum includes not only positive, zero and negative values, but also the sumof the Lyapunov indexes, that is, ∑λ_i<0, proving once again that the short-rangeweather attractor in China's monsoon areas is a form of chaotic movement. As the sumof the positive Lyapunov indexes reflects the overall exhalation of the system,it is theo-retically proved that the sum is equal to the Kolmogora entropy of the system. In thispaper, the sum of the positive indexes sum from λ_i>0λ_i=K=0. 110405 is acquired when the delayedtime τ=5, the parameter m=2,and the number of dimensions d_M=9. This is close tothe predictable time and also in good agreement with the result in the literature[2] bythe authors of the present work.
出处
《南京气象学院学报》
CSCD
1992年第1期47-56,共10页
Journal of Nanjing Institute of Meteorology
关键词
混沌
时间序列
延拓相空间
指数谱
Chaotic time series
continuation phase space
Lyapunov index spectrum
