归一化KLD系数及多维序列相关和同步的检测

提出了KLD系数和归一化KLD系数来刻画多维序列的相关结构, 以解决KLD维密度固有的局限性. 利用完全相关和完全不相关的多维序列, 导出KLD维密度的上界和下界函数, 进而导出KLD系数的上界和下界, 在此基础上提出归一化KLD系数. 解析分析和数值仿真都证明, 多维序列相关结构的变化会引起归一化KLD系数线性的变化. 数值仿真还证明, 即使多维序列中仅有其中的两个时间序列的相关结构发生改变, 归一化KLD系数仍能灵敏地检测到. 不仅如此, 归一化KLD系数还可用于非平稳时间序列的分析. 耦合映象格子的数值仿真结果表明, 归一化KLD系数还能够分析非线性系统的相关结构.

The normalized KLD coefficient and its application in detection of correlation and synchronization from multivariable series

The KLD coefficient and the normalized KLD coefficient are proposed to characterize the correlation of multivariable series in order to overcome the intrinsic limitations of the KLD dimension density. Using the uncorrelated or perfectly correlated multivariable series, the upper and the lower bound functions of the KLD dimension density, and furthermore the upper and the lower bounds of the KLD coefficient are analytically deduced. Then, the normalized KLD coefficient is proposed in the paper. The analyses and numerical simulations prove that the changes of correlation of multivariable series can lead to linear variation of the normalized KLD coefficient. The simulations also prove that the normalized KLD coefficient can detect the changes of correlation sensitively, even if these are induced by only two channels of multivariable series. Furthermore, the normalized KLD coefficient can be used to analyze the nonstationary time series. The simulation results of coupled map lattice prove that the normalized KLD coefficient can also be used for the nonlinear system analysis.