Observation Data Based On The Complexity Of The Nonlinear Space-time Distribution Characteristics

The complexity series of the logistic equation and the Lorenz model were respectively calculated in this paper using a dynamical nonlinear analysis method for time series -Lemper-Ziv complexity algorithm, and the physical implication of Lemper-Ziv complexity is also discussed. The results show that for logistic equation, the complexity is different obviously when the complicated degree of the time series is variational; and for Lorenz model, i.e. its x-, y-, and z-portion, their complexity are all chaostic and are all consisted of many cycles whose swings are almost same and the length are distinct; the result reflects that the internal quasi-periodicity. Further investigations indicate that when different window lengths were selected, characters of the complexity series for a given time series are basically the same, and exists the coherency between the jumps of the complexity series and the jumps of the time series. This paper presents, one can judge the characteristic of a time series by calculating its complexity, and this may be useful to predict the kinetic frame work of one time series.The complexity series of the Guliya (Tibetan plateau) ice core and Shihua cave (Beijing) stalagmite proxy records were respectively calculated in this paper using a dynamical nonlinear analysis method for time series -Lernper-Ziv complexity algorithm, and the physical implication of Lemper-Ziv complexity and its meaning in the study of climate change are also discussed. The wavelet analysis results show that distinctive quasi-periods of 780-, 380-, 160-, and 105-year resided in the complexity series. Further investigations indicate that when different window lengths were selected, characters of the complexity series for a given time series are basically the same, and exists the coherency between the jumps of the complexity series and the climatic jumps on various timescales. This paper presents, for the first time, the oscillation on 380-year timescale in the recent millennium, with the amplitude decaying and the intrinsic period reducing. The complexity of the time series has gradually reduced since 1900. For the complexity of the stalagmite data, existed the quasi-equal-amplitude oscillation after 1920, which is similar with the circumstances of the warming epochs over China in the middle sixth century and the middle twelfth century. Consequently, the reason for the warming in the twentieth century remains to be further studied.The conditional entropy of two symbolic sequences which are encoded faithfully from two different time series is minimized at the zero relative shifts of the two time series if the two time series have their origins in same underlying dynamics. This technique is also useful in studying the delayed coupling between different time series. Applications are made to the temperature data derived from five meteorological stations in China, namely Shanghai, Nantong, Changzhou, Nanjing and Hangzhou in order to judge the commonality of their underlying dynamics, and gain the relative strength of the dynamics coupling between different variables ,and also extract the implicit delayed information in the dynamics.A new method named "permutation entropy" for detecting dynamical changes in time series was used to analysis the day-to-day temperature time series of north china from 1960a-2000a, we detected three abrupt climate changes in the mid 1970s,in the early 1980s. Farther analysis by using Empirical Mode Decomposition to decompose the permutation entropy, the result shows that the approximate 10a cycle is most important. so we can give the conclusion that northern china suffered three abrupt climate changes in the mid 1970s,in the early 1980s , and moreover the the approximate 10a cycle induced the climate changes directly.