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Differential symbolic entropy in nonlinear dynamics complexity analysis

Differential symbolic entropy, a measure for nonlinear dynamics complexity, is proposed in our contribution. With flexible controlling parameter, the chaotic deterministic measure takes advantage of local nonlinear dynamical information among three adjacent elements to extract nonlinear complexity. In nonlinear complexity detections of chaotic logistic series, DSEn (differential symbolic entropy) has satisfied complexity extractions with the changes of chaotic features of logistic map. In nonlinear analysis of real-world physiological heart signals, three kinds of heart rates are significantly distinguished by DSEn in statistics, healthy young subjects > healthy elderly people > CHF (congestive heart failure) patients, highlighting the complex-losing theory of aging and heart diseases in cardiac nonlinearity. Moreover, DSEn does not have high demand on data length and can extract nonlinear complexity at short data sets; therefore, it is an efficient parameter to characterize nonlinear dynamic complexity.