基于复杂度分析logistic映射和Lorenz模型的研究

采用三次粗粒化方法得到了logistic映射和Lorenz模型的符号序列，运用动态非线性时间序 列分析方法——Lemper-Ziv复杂度，分别对两组符号序列进行了对比分析.对于logistic映 射，其复杂度反映了时间序列的演化；Lorenz模型三个分量的复杂度序列都具有混沌性质， 即由许多振幅非常接近而长度完全不同的循环所组成，反映了Lorenz模型内在的准周期特性 .进一步研究发现，当取不同的窗口长度时，复杂度序列的特征基本相同，并且复杂度反映 了时间序列的时空特性.因此，可以借助复杂度的计算来反演观测资料的动力学结构. 关键词： 三次粗粒化 Lemper-Ziv复杂度 logistic映射 Lorenz模型

Investigation about the Lorenz model and logistic equation based on the complexity

The complexity series of the logistic equation and the Lorenz model were respectively calculated using a dynamical nonlinear analysis method for time series— —Lemper-Ziv complexity algorithm, and the physical implication of Lemper-Ziv co mplexity is also discussed. Results show that for the logistic equation, the com plexity is obviously different when the complicated degree of the time series i s variational; and for Lorenz model, i.e. its x-, y-, and z-portions, th eir complexities are all chaotic and are all composed of many cycles whose swings are almost the same and the lengths are different. The result reflects the in ternal quasi-periodicity. Further investigations indicate that when different wi ndow lengths are selected, the characters of the complexity series for a given t ime series are basically the same, and there exists a coherency between the jump s of the complexity series and the jumps of the time series. Thus one can judge the characteristic of a time series by calculating its complexity. This may be u seful to predict the kinetic behavior of a time series.