基于C-C算法的混沌吸引子的相空间重构技术

Phase-space reconstruction technology of chaotic attractor based on C-C method

基于混沌理论可以检测心率失常、分析脑电变化,发现复杂信号的特性。相空间重构是进行混沌分析,从几何和信息论角度计算混沌特性的必要步骤。相空间重构是有效的展现混沌吸引子动力学特性的一种方法。该方法要构造一个非线性时间序列的嵌入,选择合适的时间延迟。C-C算法结合了自相关函数和互信息方法的优点,既能有效减少计算量,又能保持系统的非线性特征。本文运用C-C算法进行相空间重建,考察通过C-C算法获得的最优延迟函数。在理论分析的基础上,本文将C-C算法实际应用于洛仑兹吸引子和一组实测心电信号的相空间重构,说明相空间重构的原理与使用。经过相空间重构,可以为进一步的混沌信号分析提供关键的嵌入维数和延迟时间等参数。

Chaos theory can be used to detect arrhythmia, analyze EEG and find the characteristics of complex signal. Phase space reconstruction is the key steps for analyzing chaos characteristics from geometry and information theory. Phase space reconstruction is an effective method to develop dynamic characteristic of the chaotic attractor. In order to embed a nonlinear time series, we must choose an appropriate delay time C-C method combines the strengths of autocorrelation function and mutual information method. It not only can re- duce computation cost effectively, but also can maintain the dynamic characteristic of system. In this paper, C-C method is used to choose the optimal delay time. On basis of the theoretical analysis, the paper also applies the C-C method to reconstruct the Lorenz attractor and ECG Signals.