Quantifying entropy using recurrence matrix microstates

Corso, Gilberto; Prado, Thiago de Lima; Lima, Gustavo Zampier dos Santos; Kurths, Jürgen; Lopes, S. R.

doi:10.1063/1.5042026

Cited by 45 publications

(46 citation statements)

References 22 publications

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“…For both cases we conclude that the new method identify and quantify a new cause/effect relation where changes occurring in the time series PDF can be related directly to variations of complex behavior including the possibility to display short and long time correlations. Finally, it is worth to mention that due to its computation methodology [6], recurrence entropy is fast evaluated for arbitrary long real-world time series, leading to robust parameter-free way to process data.…”

Section: Discussionmentioning

confidence: 99%

“…At first sight, M should be larger than the quantity of all possible microstates 2 N 2 , but as observed in [6] the number of microstates effectively populated is small and the convergence of Eq. 2 is fast.…”

Section: The Recurrence Entropymentioning

confidence: 95%

“…In the case of N = 2 our microstates A(ε) will be binary numbers composed of four elements (0 or 1), namely a 2 × 2 binary matrix expressing the cross-recurrences among a 10 and a L , a 10 , and a L+1 , a 11 and a L and, finally, a 11 , and a L+1 . For a large enough randomly selected number of samples M , the recurrence entropy S can be adequately computed by [6]…”

Section: The Recurrence Entropymentioning

confidence: 99%

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Parameter-free quantification of stochastic and chaotic signals

Lopes

Prado

Corso

et al. 2020

Chaos, Solitons & Fractals

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Recurrence entropy (S) is a novel time series complexity quantifier based on recurrence microstates. Here we show that max(S) is a parameter-free quantifier of time correlation of stochastic and chaotic signals, at the same time that it evaluates property changes of the probability distribution function (PDF) of the entire data set. max(S) can distinguish distinct temporal correlations of stochastic signals following a power-law spectrum, P (f ) ∝ 1/f α even when shuffled versions of the signals are used. Such behavior is related to its ability to quantify distinct subsets embedded in a time series. Applied to a deterministic system, the method brings new evidence about attractor properties and the degree of chaoticity. The development of a new parameter-free quantifier of stochastic and chaotic time series opens new perspectives to stochastic data and deterministic time series analyses and may find applications in many areas of science.

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Section: Discussionmentioning

confidence: 99%

Section: The Recurrence Entropymentioning

confidence: 95%

Section: The Recurrence Entropymentioning

confidence: 99%

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Parameter-free quantification of stochastic and chaotic signals

Lopes

Prado

Corso

et al. 2020

Chaos, Solitons & Fractals

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“…In order to understand this, it is important to note that this entropy is conceptually different from other common entropic characteristics used in nonlinear time series analysis, exhibiting increases if the observed dynamics becomes more regular (Letellier, 2006). Other variants of recurrence plot based entropy measures have been developed recently to account for this conceptual ambiguity (Letellier, 2006;Eroglu et al, 2014;Corso et al, 2018), but have not yet become standard tools in applications of RQA and therefore not been used in the present work.…”

Section: Recurrence Measures At Different Timescales: Quiet Vs Stormmentioning

confidence: 99%

Disentangling nonlinear geomagnetic variability during magnetic storms and quiescence by timescale dependent recurrence properties

Alberti

Lekscha

Consolini

et al. 2020

J. Space Weather Space Clim.

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Understanding the complex behavior of the near-Earth electromagnetic environment is one of the main challenges of Space Weather studies. This includes both the correct characterization of the different physical mechanisms responsible for its configuration and dynamics as well as the efforts which are needed for a correct forecasting of several phenomena. By using a nonlinear multi-scale dynamical systems approach, we provide here new insights into the scale-to-scale dynamical behavior of both quiet and disturbed periods of geomagnetic activity. The results show that a scale-dependent dynamical transition occurs when moving from short to long timescales, i.e., from fast to slow dynamical processes, the latter being characterized by a more regular behavior, while more dynamical anomalies are found in the behavior of the fast component. This suggests that different physical processes are typical for both dynamical regimes: the fast component, being characterized by a more chaotic and less predictable behavior, can be related to the internal dynamical state of the near-Earth electromagnetic environment, while the slow component seems to be less chaotic and associated with the directly driven processes related to the interplanetary medium variability. Moreover, a clear difference has been found between quiet and disturbed periods, the former being more complex than the latter. These findings support the view that, for a correct forecasting in the framework of Space Weather studies, more attention needs to be devoted to the identification of proxies describing the internal dynamical state of the near-Earth electromagnetic environment.

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“…It is known that the mean field of a phase synchronized network has a "periodic" oscillation where the amplitude is bigger than in an unsynhcronized case, as observed in [11,26]. This approach makes an experimental validation possible since the recurrence quantification analysis is able to analyze experimental time series [43][44][45][46].…”

Section: Introductionmentioning

confidence: 99%

Investigation of Details in the Transition to Synchronization in Complex Networks by Using Recurrence Analysis

Budzinski

Boaretto

Prado

et al. 2019

MCA

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The study of synchronization in complex networks is useful for understanding a variety of systems, including neural systems. However, the properties of the transition to synchronization are still not well known. In this work, we analyze the details of the transition to synchronization in complex networks composed of bursting oscillators under small-world and scale-free topologies using recurrence quantification analysis, specifically the determinism. We demonstrate the existence of non-stationarity states in the transition region. In the small-world network, the transition region denounces the existence of two-state intermittency.

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Quantifying entropy using recurrence matrix microstates

Cited by 45 publications

References 22 publications

Parameter-free quantification of stochastic and chaotic signals

Parameter-free quantification of stochastic and chaotic signals

Disentangling nonlinear geomagnetic variability during magnetic storms and quiescence by timescale dependent recurrence properties

Investigation of Details in the Transition to Synchronization in Complex Networks by Using Recurrence Analysis

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