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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。
A new method to study unknown system dynamics from experimental time series based on reconstructed phase space is proposed. The concept of system qualitative state and qualitative behavior in the reconstructed phase space is defined. According to the system dynamics, the fuzzy clustering method is modified to automatically extract the qualitative state of the system. Based on these qualitative states, two representation methods of qualitative behavior of the system are given: the qualitative sequence diagram and the state transition diagram. The proposed method is simulated by using the time series generated by Lorenz system and epileptic EEG time series respectively. The results show that the proposed method can effectively extract the qualitative states of the system and each vector has a high degree of similarity. Both methods of qualitative behavior of the system can accurately characterize the nonlinear dynamics in the system behavior.