华南沿海明代自然灾害的时间序列分析Ⅱ.混沌分析

A TIME SERIES ANALYSIS ON NATURAL DISASTERS ALONG SOUTH CHINA COAST DURING MING DYNASTY Ⅱ CHAOTIC CHARACTERISTIC ANALYSIS

对我国明代华南沿海自然灾害发生次数的混沌特征分析发现 ,嵌入维数取不同值时均存在分形特征 ,且反映这种分形特征的关联维数随着嵌入维数逐渐增大而趋于一个稳定值。稳定的关联维数为 2 8,相应的饱和嵌入维数为 1 0。关联维数的稳定值为分数 (2 8)反映了控制明代华南沿海自然灾害发生次数的动力系统是一个混沌系统。构筑该系统最少需要 3个自由变量 ,最多需要 1 0个。对反映该混沌系统混沌特征强度的指标———Kolmogorov熵K值进行了计算 ,发现当嵌入维数逐渐增大到 7时K值开始稳定于 0 3 8,由此得到我国明代华南沿海自然灾害发生次数这一时间序列的可预报时间平均长度为 2 6a。

An analysis on chaotic characteristics of the time series of natural disasters that happened every year in the coastal region of South China during Ming Dynasty from 1368 to 1644 A D.is conducted.It is found that for every embedded dimension m ,the time series shows fractal characteristics.The correlation fractal dimension increases with m at first and then,when m reaches the value of 10,becomes stable around the value of 2 8.These indicate that the dynamic system controlling the numbers of natural disasters that happened every year in the coastal region of South China during Ming Dynasty is of chaotic characteristics.To establish the system,at least 3 and at most 10 uncorrelated variables are needed.The Kolmogorov entropy K of this chaotic system is also calculated based on G P method.It is found that when embedded dimension m reaches 7, K tends to stabilize around the value of 0 38.This suggests that for the time series of the numbers of natural disasters,the average predictable time period is 2 6 years.