非线性动力学复杂性分析中的双符号联合熵
Double symbolic joint entropy in nonlinear dynamic complexity analysis
摘要：
符号化是符号动力学分析的基础，本文将符号化分为全局静态和局部动态两种方法，并通过联合熵将它们结合起来进行非线性动力学复杂性分析。两种全局静态方法，Wessel N.符号熵和基尺度熵以及两个局部熵，即置换和微分熵的符号化，构成了四个双符号联合熵，它们在混沌模型、Logistic和Henon映射序列中具有精确的复杂性检测。在各种心率变异性的非线性动力学分析中，健康青年人的心率复杂度高于健康老年人，充血性心力衰竭（CHF）患者的心率联合熵值最低。通过双符号联合熵对单个符号熵进行改进，其中基尺度符号化和差分符号化的组合具有最佳的复杂度分析。测试结果证明了双符号联合熵在非线性动态复杂性分析中的可行性。
英文摘要：
Symbolizations, the base of symbolic dynamic analysis, are classified as global static and local dynamic approaches which are combined by joint entropy in our works for nonlinear dynamic complexity analysis. Two global static methods, symbolic transformations of Wessel N. symbolic entropy and base-scale entropy, and two local ones, namely symbolizations of permutation and differential entropy, constitute four double symbolic joint entropies that have accurate complexity detections in chaotic models, logistic and Henon map series. In nonlinear dynamical analysis of different kinds of heart rate variability, heartbeats of healthy young have higher complexity than those of the healthy elderly, and congestive heart failure (CHF) patients are lowest in heartbeats' joint entropy values. Each individual symbolic entropy is improved by double symbolic joint entropy among which the combination of base-scale and differential symbolizations have best complexity analysis. Test results prove that double symbolic joint entropy is feasible in nonlinear dynamic complexity analysis.
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