Recurrence Plots for the Analysis of Complex Systems

Norbert Marwan, M Carmen Romano , Marco Thiel, Jurgen Kurths

Research output: Contribution to journalArticle

1569 Citations (Scopus)

Abstract

Recurrence is a fundamental property of dynamical systems, which can be exploited to characterise the system's behaviour in phase space. A powerful tool for their visualisation and analysis called recurrence plot was introduced in the late 1980's. This report is a comprehensive overview covering recurrence based methods and their applications with an emphasis on recent developments. After a brief outline of the theory of recurrences, the basic idea of the recurrence plot with its variations is presented. This includes the quantification of recurrence plots, like the recurrence quantification analysis, which is highly effective to detect, e.g., transitions in the dynamics of systems from time series. A main point is how to link recurrences to dynamical invariants and unstable periodic orbits. This and further evidence suggest that recurrences contain all relevant information about a system's behaviour. As the respective phase spaces of two systems change due to coupling, recurrence plots allow studying and quantifying their interaction. This fact also provides us with a sensitive tool for the study of synchronisation of complex systems. In the last part of the report several applications of recurrence plots in economy, physiology, neuroscience, earth sciences, astrophysics and engineering are shown. The aim of this work is to provide the readers with the know how for the application of recurrence plot based methods in their own field of research. We therefore detail the analysis of data and indicate possible difficulties and pitfalls.

Original languageEnglish
Pages (from-to)237-329
Number of pages93
JournalPhysics Reports
Volume438
Issue number5-6
DOIs
Publication statusPublished - 12 Jan 2007

Keywords

  • data analysis
  • recurrence plot
  • nonlinear dynamics
  • time-series analysis
  • chaotic electrochemical oscillators
  • quantification analysis
  • phase synchronization
  • strange attractors
  • dynamical-systems
  • generalized synchronization
  • poincare recurrences
  • periodic-orbits
  • correlation dimension

Cite this

Recurrence Plots for the Analysis of Complex Systems. / Marwan, Norbert; Romano , M Carmen; Thiel, Marco; Kurths, Jurgen.

In: Physics Reports, Vol. 438, No. 5-6, 12.01.2007, p. 237-329.

Research output: Contribution to journalArticle

Marwan, Norbert ; Romano , M Carmen ; Thiel, Marco ; Kurths, Jurgen. / Recurrence Plots for the Analysis of Complex Systems. In: Physics Reports. 2007 ; Vol. 438, No. 5-6. pp. 237-329.
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