Inferring Indirect Coupling by Means of Recurrences

Zou, Yong; Romano, M. Carmen; Thiel, Marco; Marwan, Norbert; Kurths, Jürgen

doi:10.1142/s0218127411029033

Cited by 44 publications

(27 citation statements)

References 30 publications

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“…In this context, we note that the recurrence characteristics employed in the present work have not been selected to unveil any cause‐effect relationships. For the latter purpose, there exist further sophisticated approaches based upon recurrence plots (e.g., based on conditional recurrence probabilities [Romano et al, ; Zou et al, ] or intersystem recurrence networks [Feldhoff et al, ]) or related phase space‐based techniques like convergent cross‐mapping (Sugihara et al, ). However, applying such approaches has been clearly beyond the scope of the present work.…”

Section: Discussionmentioning

confidence: 99%

Recurrence‐Based Quantification of Dynamical Complexity in the Earth's Magnetosphere at Geospace Storm Timescales

et al. 2019

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Magnetic storms are the most prominent global manifestations of out‐of‐equilibrium magnetospheric dynamics. Investigating the dynamical complexity exhibited by geomagnetic observables can provide valuable insights into relevant physical processes as well as temporal scales associated with this phenomenon. In this work, we utilize several innovative data analysis techniques enabling a quantitative nonlinear analysis of the nonstationary behavior of the disturbance storm time (Dst) index together with some of the main drivers of its temporal variability, the VBSouth electric field component, the vertical component of the interplanetary magnetic field, Bz, and the dynamic pressure of the solar wind, Pdyn. Using recurrence quantification analysis and recurrence network analysis, we obtain several complementary complexity measures that serve as markers of different physical processes underlying quiet and storm time magnetospheric dynamics. Our approach discriminates the magnetospheric activity in response to external (solar wind) forcing from primarily internal variability and highlights the case‐specific nature of interdependencies between the Dst index and its potential drivers that need to be accounted for in future improved space weather forecasting models.

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Section: Discussionmentioning

confidence: 99%

Recurrence‐Based Quantification of Dynamical Complexity in the Earth's Magnetosphere at Geospace Storm Timescales

et al. 2019

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“…Distance-based characteristics allowing one to reliably detect directional couplings between different variables have been developed and applied by various authors, e.g., [76][77][78][79][80][81][82]. A specific class of approaches is based on the recurrence matrix, making use of conditional recurrence probabilities [83,84] or asymmetries in coupled network statistics [85]. Since these methods are not within the focus of this review, we refer to the aforementioned references for further details.…”

Section: Causality From Phase Space Methodsmentioning

confidence: 99%

Statistical Mechanics and Information-Theoretic Perspectives on Complexity in the Earth System

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et al. 2013

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This review provides a summary of methods originated in (non-equilibrium) statistical mechanics and information theory, which have recently found successful applications to quantitatively studying complexity in various components of the complex Entropy 2013, 15 4845 system Earth. Specifically, we discuss two classes of methods: (i) entropies of different kinds (e.g., on the one hand classical Shannon and Rényi entropies, as well as non-extensive Tsallis entropy based on symbolic dynamics techniques and, on the other hand, approximate entropy, sample entropy and fuzzy entropy); and (ii) measures of statistical interdependence and causality (e.g., mutual information and generalizations thereof, transfer entropy, momentary information transfer). We review a number of applications and case studies utilizing the above-mentioned methodological approaches for studying contemporary problems in some exemplary fields of the Earth sciences, highlighting the potentials of different techniques.

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“…In addition to synchronization analysis based on real time series, it remains to be an interesting topic to identify the driver-response relationship, especially to identify indirect from direct coupling directions [46][47][48][49]. From the viewpoint of ordinal pattern perspective, it is possible to combine ordinal recurrence plots [50] and cross and joint ordinal partition transition network approaches to tackle this problem.…”

Section: Discussionmentioning

confidence: 99%

Cross and joint ordinal partition transition networks for multivariate time series analysis

et al. 2018

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We propose to construct cross and joint ordinal pattern transition networks from multivariate time series for two coupled systems, where synchronizations are often present. In particular, we focus on phase synchronization, which is one of prototypical scenarios in dynamical systems. We systematically show that cross and joint ordinal patterns transition networks are sensitive to phase synchronization. Furthermore, we find that some particular missing ordinal patterns play crucial roles in forming the detailed structures in the parameter space whereas the calculations of permutation entropy measures often do not. We conclude that cross and joint ordinal partition transition network approaches provide complementary insights to the traditional symbolic analysis of synchronization transitions.

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Inferring Indirect Coupling by Means of Recurrences

Cited by 44 publications

References 30 publications

Recurrence‐Based Quantification of Dynamical Complexity in the Earth's Magnetosphere at Geospace Storm Timescales

Recurrence‐Based Quantification of Dynamical Complexity in the Earth's Magnetosphere at Geospace Storm Timescales

Statistical Mechanics and Information-Theoretic Perspectives on Complexity in the Earth System

Cross and joint ordinal partition transition networks for multivariate time series analysis

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