Identifying coupling directions by recurrences

Yong Zou*, M Carmen Romano, Marco Thiel, Jürgen Kurths

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapter

4 Citations (Scopus)


The identification of the coupling direction from measured time series taking place in a group of interacting components is an important challenge for many experimental studies. In Part I of this chapter, we introduce a method to detect and quantify the asymmetry of the coupling between two interacting systems based on their recurrence properties. This method can detect the direction of the coupling in weakly as well as strongly coupled systems. It even allows detecting the asymmetry of the coupling in the more challenging case of structurally different systems and it is very robust against noise. We also address the problem of detecting the asymmetry of the coupling in passive experiments, i.e., when the strength of the coupling cannot be systematically changed, which is of great relevance for the analysis of experimental time series. Part II of this chapter hinges on a generalisation of conditional probability of recurrence to the case of multivariate time series where indirect interactions might be present. We test our method by an example of three coupled Lorenz systems. Our results confirm that the proposed method has much potential to identify indirect coupling.

Original languageEnglish
Title of host publicationRecurrence Quantification Analysis
Subtitle of host publicationTheory and Best Practices - Part I
EditorsCharles L Webber Jr, Norbert Marwan
Number of pages35
ISBN (Electronic)978-3-319-07155-8
ISBN (Print)9783319071541
Publication statusPublished - 12 Aug 2014

Publication series

NameUnderstanding Complex Systems
ISSN (Print)18600832
ISSN (Electronic)18600840


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