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Title: Recurrence networks-a novel paradigm for nonlinear time series analysis
Authors: Donner, R.V.Zou, Y.Donges, J.F.Marwan, N.Kurths, J.
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Issue Date: 2010
Published in: New Journal of Physics Vol. 12 (2010)
Publisher: College Park, MD : Institute of Physics Publishing
Abstract: 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. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.
Keywords: Adjacency matrices; Average path length; Centrality measures; Clustering coefficient; Complex networks; Complex systems; Dynamical complexity; Existing method; In-phase; matrix; Matrix yields; Network-based; New approaches; Nonlinear time-series analysis; Novel interpretation; Phase space densities; Quantitative characteristics; Statistical properties; Topological properties; Circuit theory; Dynamical systems; Large scale systems; Time series; Topology; Time series analysis
DDC: 530
License: CC BY-NC-SA 3.0 Unported
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