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Chaos, 28(8), 083108p. (2018) DOI:10.1063/1.5042026
We conceive a new recurrence quantifier for time series based on the concept of information entropy, in which the probabilities are associated with the presence of microstates defined on the recurrence matrix as small binary submatrices. The new methodology to compute the entropy of a time series has advantages compared to the traditional entropies defined in the literature, namely, a good correlation with the maximum Lyapunov exponent of the system and a weak dependence on the vicinity threshold parameter. Furthermore, the new method works adequately even for small segments of data, bringing consistent results for short and long time series. In a case where long time series are available, the new methodology can be employed to obtain high precision results since it does not demand large computational times related to the analysis of the entire time series or recurrence matrices, as is the case of other traditional entropy quantifiers. The method is applied to discrete and continuous systems.
A large number of quantifiers of complexity based on data can be found in the literature. In general, all these quantities were developed to distinguish regular, chaotic, and random properties of a time series. The knowledge of these properties is fundamental since it has been reported that complexity is an important characteristic of data of heart and brain signals, stock market, climatology, seismology, etc. The main types of complexity measures are entropies, Lyapunov's exponents, and fractal dimensions. Here, we develop a new entropy based on recurrence properties of a time series. The new recurrence entropy has a good correlation with the maximum Lyapunov exponent of the system and a weak dependence on the vicinity threshold parameter, a critical parameter on recurrence analysis. Furthermore, the new method works adequately even for small segments of data, bringing consistent results for short and long time series.
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