标题： 混沌序列的TQ复杂度估计 显示英文标题

标题： Estimation of the TQ-complexity of chaotic sequences

摘要： 一种新的方法被提出，用于在状态扩展空间中轨迹形状的基础上，对多维离散序列的复杂性进行定量估计。 该方法基于对序列结构特性的研究，适用于对混沌序列和随机序列的复杂性进行估计。 它是建立在作者之前提出的多维离散序列和映射的符号CTQ分析方法基础上的。 所提出的算法不仅处理符号出现的频率，还考虑了它们的顺序。 给出了一个示例（金融时间序列），以展示所开发工具的应用。 显示英文摘要

摘要： A new approach is proposed to the quantitative estimation of the complexity of multidimensional discrete sequences in terms of the shapes of their trajectories in the extended space of states. This approach is based on the study of the structural properties of sequences and is suitable for estimating the complexity of both chaotic and stochastic sequences. It is constructed on the method, proposed earlier by the author, of symbolic CTQ-analysis of multidimensional discrete sequences and mappings. The algorithm proposed manipulates not only the frequency of occurrence of symbols, but also takes into account their sequence order. An example (financial time series) is given that demonstrates the application of the tools developed.