Abstract
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.
Highlights
Heart rate variability (HRV), the variation in beat-to-beat intervals represented by RR or NN interval,[1] displays irregular and non-stationary behaviors whose nonlinear dynamics provide valuable information for cardiac scientific and clinical researches.[2,3]
These symbolic transformations are classified into two groups, global static and local dynamic methods.[12]
Global static methods perform symbolization according to different sequences intervals which are identified by several parameters obtained from the whole sequence, and local dynamical approaches, on other hands, take contribution of local adjacent elements’ relationships to carry on symbolic representation
Summary
Heart rate variability (HRV), the variation in beat-to-beat intervals represented by RR or NN interval,[1] displays irregular and non-stationary behaviors whose nonlinear dynamics provide valuable information for cardiac scientific and clinical researches.[2,3] To measure its nonlinear dynamical features, some complexity parameters, such as fractal dimensions, Lyapunov exponents, geometric and entropy methods et al, are proposed.[4,5,6] Symbolic dynamic analysis, a kind of fast, simple and efficient method, provides rigorous ways to analyze nonlinear dynamics.[7]. In order to make efficient use of the two types of symbolizations, we apply joint entropy to combine them for nonlinear dynamic complexity. In our contributions to combine the two kinds of symbolic transformations, we conduct global static and local dynamic symbolic transformation simultaneously, and apply the two kinds of symbolizations’ joint entropy to nonlinear dynamic analysis of classical nonlinear chaotic models and three kinds of real-world HRV
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