时间序列重构相空间中系统定性行为建模与仿真

提出了一种以重构相空间为基础,从实验时间序列研究未知系统动力学的新方法.定义了重构相空间中系统定性状态和定性行为的概念,根据系统动力学特性对模糊聚类方法进行改造,用于自动提取系统的定性状态.基于这些定性状态,给出了系统定性行为的两种表示方法:时序定性状态图和定性状态转移图.分别运用Lorenz系统产生的时间序列和癫痫脑电时间序列对提出的方法进行仿真实验,结果表明,该方法能有效提取系统的定性状态,每个定性状态中的向量之间具有高度的相似性.系统定性行为的两种表示方法均能准确地刻画系统行为中的非线性动力学特征.

Qualitative Behavior Modeling and Simulation of Underlying System in Phase Space Reconstructed from Experimental Time Series

A novel method based on phase-space reconstruction was proposed to analyze underlying system dynamics from experimental time series.The conceptions of qualitative state and qualitative behavior of underlying system in reconstructed phase space were defined.The qualitative states were extracted by improved fuzzy clustering in terms of the properties of system dynamics.Based on these states,the qualitative behavior was represented in two ways:the plot of temporal qualitative state and the graph of qualitative state transition.The time series from Lorenz system and epileptiform electroencephalogram(EEG) were tested on the proposed method.The results of simulation show that the method may efficiently extract qualitative states from phase-space trajectory.For each qualitative state,all vectors have high-similar degree.The plot and graph of qualitative behavior may exactly illustrate the process of system dynamics.