Recurrence networks—a novel paradigm for nonlinear time series analysis

By Reik V. Donner, Yong Zou, Jonathan F. Donges, Norbert Marwan, Jürgen Kurths. 2009

569 citations recorded by the source corpus.

This paper presents a new approach for analysing the structural properties of time series from complex systems. Starting from the concept of recurrences in phase space, the recurrence matrix of a time series is interpreted as the adjacency matrix of an associated complex network, which links different points in time if the considered states are closely neighboured in phase space. In comparison with similar network-based techniques the new approach has important conceptual advantages, and can be considered as a unifying framework for transforming time series into complex networks that also includes other existing methods as special cases. It has been demonstrated here that there are fundamental relationships between many topological properties of recurrence networks and different nontrivial statistical properties of the phase space density of the underlying dynamical system. Hence, this novel interpretation of the recurrence matrix yields new quantitative characteristics (such as average path length, clustering coefficient, or centrality measures of the recurrence network) related to the dynamical complexity of a time series, most of which are not yet provided by other existing methods of nonlinear time series analysis.

Subfields: Computer Networks and Communications, Economics and Econometrics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/6c719578feceabee3bf0a966583893e1814a6d39

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Citations in the corpus

Imaging Time-Series to Improve Classification and Imputation (2015, methodology): “Re-currence Networks were proposed to analyze the structural properties of time series from complex systems [ Donner et al. , 2010; 2011 ] .”
Complex network approaches to nonlinear time series analysis (2019, background): “Notably, the detection limit of UPOs should be ultimately determined by the recurrence threshold ε in conjunctionwith the RN sizeN .”
The role of fluctuating modes of autocorrelation in crude oil prices (2014, background): “The links between the nodes are defined by correlationmeasures [7–9].”
Recurrence-based time series analysis by means of complex network methods (2010, methodology): “1C) is distinctively diﬀerent from the trajectory concept that records the causal dynamic evolution of the system [Donner et al. , 2010b].”
Complex network approach for recurrence analysis of time series (2009, methodology): “We illustrate our approach with a prototypical model system and a real-world example from the Earth sciences.”
Statistical properties of visibility graph of energy dissipation rates in three-dimensional fully developed turbulence (2009, background): “ber 23, 2018 its four nearest neighbors to form a complex network [11]. There are also other mapping methods from time series to networks based on n-tuples of ﬂuctuations [12–14] or recurr ence plots [15, 16]. Lacasa et al. proposed the visibility graph algorithm, which can map all types of time ser”
Sensitivity and Nonlinearity of Thermoacoustic Oscillations (2018, methodology): “Complex networks (see the sidebar titled Representing Complex Systems Using Complex Networks) have been used to understand the dynamics underlying time-series data (Lacasa et al. 2008, Donner et al. 2010).”