Recurrence-based time series analysis by means of complex network methods

By Reik V. Donner, Michael Small, Jonathan F. Donges, Norbert Marwan, Yong Zou, Ruoxi Xiang, Jürgen Kurths. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 2010

362 citations recorded by the source corpus.

Complex networks are an important paradigm of modern complex systems sciences which allows quantitatively assessing the structural properties of systems composed of different interacting entities. During the last years, intensive efforts have been spent on applying network-based concepts also for the analysis of dynamically relevant higher-order statistical properties of time series. Notably, many corresponding approaches are closely related with the concept of recurrence in phase space. In this paper, we review recent methodological advances in time series analysis based on complex networks, with a special emphasis on methods founded on recurrence plots. The potentials and limitations of the individual methods are discussed and illustrated for paradigmatic examples of dynamical systems as well as for real-world time series. Complex network measures are shown to provide information about structural features of dynamical systems that are complementary to those characterized by other methods of time series analysis and, hence, substantially enrich the knowledge gathered from other existing (linear as well as nonlinear) approaches.

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

View Paper: https://www.semanticscholar.org/paper/737b6a58784fa98032be7fe741e58abf2673ef11

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computer Networks and Communications

In Economics and Econometrics

In Statistical and Nonlinear Physics

Citations in the corpus

The Dangers of Rounding Errors for Simulations and Analysis of Nonlinear Circuits and Systems?and How to Avoid Them (2013, background): “For a similar concept of analyzing structural features of complex systems see [20].”
Complex network approaches to nonlinear time series analysis (2019, methodology): “, considering k-nearest neighbors [54], which will be further discussed below.”
Structure and dynamics of molecular networks: A novel paradigm of drug discovery: A comprehensive review (2012, methodology): “…representations of energy landscapes (or fitness landscapes) resulting in transition networks, and in the recurrence-based time series analysis resulting in correlation networks, cycle networks, recurrence networks or visibility graphs (Doye, 2002; Rao & Caflisch, 2004; Donner et al., 2011).”
Nonlinear time-series analysis revisited. (2015, background): “Recently, recurrence plots have been interpreted in a very diﬀerent way, namely as the adjacency matrix of an undirected network 46 .”