非线性时间序列互信息与Lempel-Ziv复杂度的相关性研究

为探究非线性动力学系统的互信息和复杂度的相关性，用Logistic映射、Lorenz模型和心电RR间期的非线性时间序列作为实验数据，计算多分段延时互信息和多分段Lempel-Ziv复杂度以及它们之间的相关系数.结果表明这些序列的互信息和复杂度呈强负相关，对Logistic方程生成的201个序列的不同段互信息和不同段复杂度之间的相关系数绝对值都大于0.9162，最大达0.9923；对94个心电RR间期序列都大于0.8555，最大达0.9860.研究还发现互信息比复杂度能更敏感地表现出非线性动力系统的特征.关键词：相关系数互信息Lempel-Ziv 复杂度心电RR间期

Research on the correlation between the mutual information and Lempel-Ziv complexity of nonlinear time series

To explore the correlation between the mutual information and complexity of nonlinear dynamic system, the nonlinear time series of Logistic map, Lorenz model and cardiac RR intervals were used as the experimental data. The multi-segmented time-delayed mutual information, multi-segmented Lempel-Ziv complexity and their correlation coefficients were calculated. The results show that the mutual information of these series are strongly negatively correlated with the complexity. For the 201 series generated by Logistic equation, the absolute value of all correlation coefficients between the mutual information and the complexity of various segments are 0.9126 plus and the maximum reach to 0.9923, and for the 94 series of cardiac RR intervals, they are 0.8555 plus and the maximum reach to 0.9860. The investigations also indicate that the mutual information is more sensitive than the complexity in characterizing a nonlinear dynamic system.