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

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.