Nonlinear analysis of bivariate data with cross recurrence plots

By Norbert Marwan, Jürgen Kurths. 2002

477 citations recorded by the source corpus.

We use the extension of the method of recurrence plots to cross recurrence plots (CRP) which enables a nonlinear analysis of bivariate data. To quantify CRPs, we develop further three measures of complexity mainly basing on diagonal structures in CRPs. The CRP analysis of prototypical model systems with nonlinear interactions demonstrates that this technique enables to find these nonlinear interrelations from bivariate time series, whereas linear correlation tests do not. Applying the CRP analysis to climatological data, we find a complex relationship between rainfall and El Nino data.

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

View Paper: https://www.semanticscholar.org/paper/6992fda04ef06141bffaa9fefff15bf183275cc4

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

1. Yong Zou
2. Norbert Marwan
3. Jonathan F. Donges
4. Reik V. Donner
5. Jürgen Kurths
6. Cornelis J. Stam
7. Rick Dale
8. Michael J. Spivey

In Economics and Econometrics

1. Norbert Marwan
2. Jürgen Kurths
3. Yong Zou
4. Reik V. Donner
5. Jonathan F. Donges
6. Cornelis J. Stam
7. Rick Dale
8. Michael J. Spivey

In Statistical and Nonlinear Physics

1. Norbert Marwan
2. Yong Zou
3. Reik V. Donner
4. Jonathan F. Donges
5. Jürgen Kurths
6. Cornelis J. Stam
7. Rick Dale
8. Michael J. Spivey

Citations in the corpus

• Damage detection using multivariate recurrence quantification analysis (2006, methodology): “Recent applications of RQA include the detection of non-stationarities in human heart rate data [1], tracking bifurcations [10], detecting determinism in noisy signals [11] and examining coupling in non-linear systems [12].”
• Similarity estimators for irregular and age-uncertain time series (2013, background): “…ESF) here, but this could be expanded for other concepts, for example, based on (cross-)recurrence plots (Romano et al., 2005; Marwan et al., 2007; Marwan, 2002; Lange, 2011), recurrence networks (Feldhoff et al., 2012), convergent cross mapping (Sugihara et al., 2012) or distance measures…”
• Encounters with neighbours : current developments of concepts based on recurrence plots and their applications (2003, methodology): “This new technique is particularly efficient for the analysis of rather nonstationary, short and noisy data and was successfully applied to prototypical model systems with nonlinear interrelations (Marwan and Kurths 2002).”
• A historical review of recurrence plots (2008, unknown): “ systems. Consequently, cross recurrence quantification analysis followed. This technique can be used to detect deterministic signals [62] and to study complex interrelations between different systems [30, 35]. Here delay based variants of the RQA measures were introduced [30]. Furthermore, CRPs appe”
• Complex network approaches to nonlinear time series analysis (2019, background): “In the last decade, two different widely applicable bi- and multivariate extensions of RPs and RQA have been proposed [57]: cross-recurrence plots [97,98,189] and joint recurrence plots [99].”
• Nonlinear dynamical analysis of EEG and MEG: review of an emerging field. (2005, methodology): “A modification called cross recurrence plots has been proposed as a tool to study nonlinear interdependencies in bivariate data sets (Marwan and Kurths, 2002).”
• Unraveling the Dyad: Using Recurrence Analysis to Explore Patterns of Syntactic Coordination Between Children and Caregivers in Conversation (2006, methodology): “To construct recurrence plots, we used the Matlab CRP Toolbox (Marwan & Kurths, 2002).”