A SPECTRUM OF LYAPUNOV EXPONENTS OBTAINED FROM A CHAOTIC TIME SERIES

A complete spectrum of Lyapunov exponents (LEs) is obtained from 1970-1985 daily mean pressure measurements at Shanghai by means of a correlation matrix analysis technique and it is found that there exist LEs≥0,and 0. with their sum zero (∑λ10), thus showing the evolution of the climate-weather system represented by the series to be chaotic. The sum of positive LE is known to represent the bodily divergence of the system and the sum of these positive LEs is theoretically found to be Kolmogorov entropy of the system. This paper shows that with the time lag τ=5, the parameter m=2 and the dimensionality dM=9, the sum of the positive LEs sum from λi0λi=K=0.110405 whereupon T=1/K=9 is obtained as the predictable time scale, a result close to that acquired by the dynamic-statistical approach in early days and also in agreement with that present by the authors themselves(1991).