Complex network approach for recurrence analysis of time series

Marwan, Norbert; Donges, Jonathan F.; Zou, Yong; Donner, Reik V.; Kurths, Jürgen

doi:10.1016/j.physleta.2009.09.042

Cited by 544 publications

(442 citation statements)

References 55 publications

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“…[54][55][56] Finally, e-recurrence networks (RNs) provide a graphtheoretical framework for quantifying various aspects of the underlying attractor's geometry. 29,[57][58][59][60][61][62][63][64][65][66][67] In the following, we will use pðsÞ and K 2 for further characterizing the dynamical complexity of the observed electrochemical oscillations. For this purpose, we will restrict our attention to the first N ¼ 10 000 points of the embedded time series in order to keep the computational efforts at an acceptable level.…”

Section: -5mentioning

confidence: 99%

“…For this purpose, we utilize the concept of RNs. 57,58,61 For computational reasons, we will again restrict ourselves to networks constructed from N ¼ 10 000 state vectors in the considered reconstructed phase space and a fixed recurrence rate of RR ¼ 0.03. Specifically, for the experimental data, we can consider ensembles of randomly drawn state vectors, since RN analysis only requires a reasonable spatial sampling of the attractor, but no time information.…”

Section: Structural Attractor Characterizationmentioning

confidence: 99%

“…In this work, we will use a complementary set of RN characteristics [69][70][71] that have already demonstrated their capabilities to distinguish qualitatively different types of dynamics based on structural attractor properties 29,57,63 1. The local clustering coefficient C v quantifies the relative amount of closed triangles centered at a given vertex v (i.e., at the associated pointx v in phase space).…”

Section: -7mentioning

confidence: 99%

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Phase coherence and attractor geometry of chaotic electrochemical oscillators

Zou

Donner

Wickramasinghe

et al. 2012

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Chaotic attractors are known to often exhibit not only complex dynamics but also a complex geometry in phase space. In this work, we provide a detailed characterization of chaotic electrochemical oscillations obtained experimentally as well as numerically from a corresponding mathematical model. Power spectral density and recurrence time distributions reveal a considerable increase of dynamic complexity with increasing temperature of the system, resulting in a larger relative spread of the attractor in phase space. By allowing for feasible coordinate transformations, we demonstrate that the system, however, remains phase-coherent over the whole considered parameter range. This finding motivates a critical review of existing definitions of phase coherence that are exclusively based on dynamical characteristics and are thus potentially sensitive to projection effects in phase space. In contrast, referring to the attractor geometry, the gradual changes in some fundamental properties of the system commonly related to its phase coherence can be alternatively studied from a purely structural point of view. As a prospective example for a corresponding framework, recurrence network analysis widely avoids undesired projection effects that otherwise can lead to ambiguous results of some existing approaches to studying phase coherence. Our corresponding results demonstrate that since temperature increase induces more complex chaotic chemical reactions, the recurrence network properties describing attractor geometry also change gradually: the bimodality of the distribution of local clustering coefficients due to the attractor’s band structure disappears, and the corresponding asymmetry of the distribution as well as the average path length increase.

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Section: -5mentioning

confidence: 99%

Section: Structural Attractor Characterizationmentioning

confidence: 99%

Section: -7mentioning

confidence: 99%

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Phase coherence and attractor geometry of chaotic electrochemical oscillators

Zou

Donner

Wickramasinghe

et al. 2012

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…22,23 While time series networks can reflect the dynamical properties of time series obtained from a complex system in a smorgasbord of different ways, pyunicorn focusses on two complementary approaches: (i) Recurrence networks, 24,25 an approach closely related to recurrence quantification analysis of recurrence plots, are random geometric graphs 26,119 representing proximity relationships (links) of state vectors (nodes) in phase space (Sec. IV A).…”

Section: Network-based Time Series Analysismentioning

confidence: 99%

“…On the other hand, network-based time series analysis investigates the dynamical properties of complex systems' states based on uni-or multivariate time series data using methods from network theory. 22 Various types of time series networks have been proposed for performing this type of analysis, including recurrence networks based on the recurrence properties of phase space trajectories, [23][24][25][26] transition networks encoding transition probabilities between different phase space regions, 27 and visibility graphs representing visibility relationships between data points in a time series. [28][29][30] The purpose of this paper is to introduce the Python software package pyunicorn, which implements methods from both complex network theory and nonlinear time series analysis, and unites these approaches in a performant, modular and flexible way.…”

Section: Introductionmentioning

confidence: 99%

Unified functional network and nonlinear time series analysis for complex systems science: The`pyunicorn`package

Donges

Heitzig

Beronov

et al. 2015

Chaos

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111

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We introduce the pyunicorn (Pythonic unified complex network and recurrence analysis toolbox) open source software package for applying and combining modern methods of data analysis and modeling from complex network theory and nonlinear time series analysis. pyunicorn is a fully object-oriented and easily parallelizable package written in the language Python. It allows for the construction of functional networks such as climate networks in climatology or functional brain networks in neuroscience representing the structure of statistical interrelationships in large data sets of time series and, subsequently, investigating this structure using advanced methods of complex network theory such as measures and models for spatial networks, networks of interacting networks, node-weighted statistics or network surrogates. Additionally, pyunicorn provides insights into the nonlinear dynamics of complex systems as recorded in uni-and multivariate time series from a non-traditional perspective by means of recurrence quantification analysis (RQA), recurrence networks, visibility graphs and construction of surrogate time series. The range of possible applications of the library is outlined, drawing on several examples mainly from the field of climatology.Network theory and nonlinear time series analysis provide powerful tools for the study of complex systems in various disciplines such as climatology, neuroscience, social science, infrastructure or economics. In the last years, combining both frameworks has yielded a wealth of new approaches for understanding and modeling the structure and dynamics of such systems based on the statistical analysis of network or uni-and multivariate time series. The pyunicorn software package (available at https://github.com/pik-copan/pyunicorn) facilitates the innovative synthesis of methods from network theory and nonlinear time series analysis in order to develop novel integrated methodologies. This paper provides an overview of the functionality provided by pyunicorn, introduces the theoretical concepts behind it and provides examples in the form of selected use cases mainly in the fields of climatology and paleoclimatology.

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Holocene climate forcings and lacustrine regime shifts in the Indian summer monsoon realm

Prasad

Marwan

Eroğlu

et al. 2020

Earth Surf Processes Landf

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Extreme climate events have been identified both in meteorological and long‐term proxy records from the Indian summer monsoon (ISM) realm. However, the potential of palaeoclimate data for understanding mechanisms triggering climate extremes over long time scales has not been fully exploited. A distinction between proxies indicating climate change, environment, and ecosystem shift is crucial for enabling a comparison with forcing mechanisms (e.g. El‐Niño Southern Oscillation). In this study we decouple these factors using data analysis techniques [multiplex recurrence network (MRN) and principal component analyses (PCA)] on multiproxy data from two lakes located in different climate regions – Lonar Lake (ISM dominated) and the high‐altitude Tso Moriri Lake (ISM and westerlies influenced). Our results indicate that (i) MRN analysis, an indicator of changing environmental conditions, is associated with droughts in regions with a single climate driver but provides ambiguous results in regions with multiple climate/environmental drivers; (ii) the lacustrine ecosystem was ‘less sensitive’ to forcings during the early Holocene wetter periods; (iii) archives in climate zones with a single climate driver were most sensitive to regime shifts; (iv) data analyses are successful in identifying the timing of onset of climate change, and distinguishing between extrinsic and intrinsic (lacustrine) regime shifts by comparison with forcing mechanisms. Our results enable development of conceptual models to explain links between forcings and regional climate change that can be tested in climate models to provide an improved understanding of the ISM dynamics and their impact on ecosystems. © 2020 John Wiley & Sons, Ltd.

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Complex network approach for recurrence analysis of time series

Cited by 544 publications

References 55 publications

Phase coherence and attractor geometry of chaotic electrochemical oscillators

Phase coherence and attractor geometry of chaotic electrochemical oscillators

Unified functional network and nonlinear time series analysis for complex systems science: The`pyunicorn`package

Holocene climate forcings and lacustrine regime shifts in the Indian summer monsoon realm

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Complex network approach for recurrence analysis of time series

Cited by 544 publications

References 55 publications

Phase coherence and attractor geometry of chaotic electrochemical oscillators

Phase coherence and attractor geometry of chaotic electrochemical oscillators

Unified functional network and nonlinear time series analysis for complex systems science: Thepyunicornpackage

Holocene climate forcings and lacustrine regime shifts in the Indian summer monsoon realm

Contact Info

Product

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About

Unified functional network and nonlinear time series analysis for complex systems science: The`pyunicorn`package