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 pressuremeasurements 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 (∑λ<0), thus showing the evolution of the climate-weather system represented by theseries to be chaotic. The sum of positive LE is known to represent the bodily divergence of the system and the sum of these positive LEsis theoretically found to be Kolmogorov entropy of the system. This paper shows that with the time lag τ=5, theparameter m=2 and the dimensionality d=9, the sum of the positive LEs sum fromλ>0λ=K=0.110405 whereuponT=1 /K =9 is obtained as the predictable time scale, a result close to that acquired by the dynamic-statistical approachin early days and also in agreement with that present by the authors themselves(1991).