Lorenz系统混沌解序列可预报性的统计检验

利用Lorenz简化热对流模式产生了吸引子区域内的混沌解序列，对截取的序列进行了乎稳性和正态性检验．按照3种情形分别选取样本，并应用统计预报中的ARMA模型、多元线性回归模型、多项式回归模型和均值生成函数模型等作出项报。比较分析表明：所选取方程组产生的混池解序列，呈现非周期、非乎稳、非正态特性等极不规则的分布，导致几种统计模型对于两个不稳定平衡状态间的不确定的突变情形基本失去了预报能力，系统行为几乎无法预测，其根本原因在于系统的混沌特性。但在某一不稳定平衡状态内，序列段呈现振幅不断放大的准周期振荡，具有一定的规律性，几种统计模型预报的效果较好，说明在应用统计方法进行预报的前提下，系统行为存在着局部时段的有限的可预报性。

Statistical analysis of the predictability of the chaotic solution series of Lorenz system

By using Lorenz model, the numerical solution series with chaotic characteristics in the attractor are generated, the stationary and normal distribution tests of the solution series were operated. Analysis samples are chosen according to three conditions.Firstly the samples were fitted and forecast by using the ARMA model, the multivariate linear regression model, the polynomial regression model and the mean generating function model etc. Secondly, the root mean square errors and complex correlation coefficients of the fitting and forecast values are compared with the actual values. The analysis shows that the whole series generated are nonperiodic, unstable, abnormal and anomalistic, which causes statistical models invalid for chaotic characteristics, but in some unstable equilibrium, the parts of series chosen are regular. Four kinds of statistical models are feasible. Under the condition of using the statistic forecast methods, it is verified that systerm actions are limitedly predictable in some partial domains.