用大气湍流资料计算Lyapunov指数和分数维

COMPUTATION OF LYAPUNOV EXPONENT AND FRACTAL DIMENSION BY USING ATMOSPHERIC TURBULENT DATA

中文摘要:

      本文从浑沌和奇怪吸引子的遍历理论出发,用大气湍流资料计算了Lyapunov指数(LE)和分数维数(FD)。结果表明,在一定参数下,由所用资料算得第一个指数LE₁为+0.1—+0.4,FD为2.3。根据计算结果讨论了大气运动的浑沌状态。

英文摘要:

      Basing on the ergodic theory on chaos and strange attractors, Lyapunov exponent (LE) and fractal dimension (FD) are computed by using the atmospheric turbulent data X (t).In the case of fixed evolution time, the computation technique of LE can be separated into two parts: reconstruction of embedding phase space R(m) from X(t) and computation of LE1 with respect to various parameters. The algorithm for FD can also be separated: reconstruction of R(m) from X(t) and computation of relation integral and dimension for approching to FD. In our work for m=3, LE₁ is +0.1—+0.4 and FD is 2.1-2.7. These results are in accordence with theoretical analysis. Moreover, the relations of LE and Fp to some control para meters are represented, respectively.