太阳黑子数时间序列的分形研究及预测

The Fractal Research and Predicating on the Time Series of Sunspot Relative Number

本文应用非线性动力系统理论分析了１８９１年１月至１９９６年１２月间太阳黑子月平均数变化的动力行为及其可预测性·计算了它的分形维数（Ｄ＝３３±０２）·确定了预测的嵌入维数［２×Ｄ＋１］＝７；计算了Ｌｙａｐｕｎｏｖ指数（λ１＝０８６３），揭示了该系统的混沌特性；并计算了Ｋｏｌｍｏｇｏｒｏｖ熵（Ｋ＝００２６０），用以从理论上分析这组数据可预报的时间尺度·最后根据分析的结果。

In this paper, with the theory of nonlinear dynamic systems, It is analyzed that the dynamic behavior and the predictability for the monthly mean variations of the sunspot relative number recorded from January 1891 to December 1996. In the progress, the fractal dimension (D=3 3±0 2) for the variation process was computed. This helped us to determine the embedded dimension =7. By computing the Lyapunov index (λ 1=0 863), it was indicated that the variation process is a chaotic system. The Kolmogorov entropy (K=0 0260) was also computed, which provides, theoretically, the predicable time scale. And at the end, according to the result of the analysis above, an experimental predication is maded, whose date was a part cut from the sample date.