Nonlinear analysis of bivariate data with cross recurrence plots
Physics Letters APublished 1 September 2002Open access
Norbert Marwan, Jürgen Kurths
Citations483
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
Abstract
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.
Keywords
Computer ScienceEconomics, Econometrics and FinancePhysics and Astronomy
American Journal of Physics<i>The Fractal Geometry of Nature</i>
21,750 Citations1983Benoît B. Mandelbrot, John Wheeler
Journal of the Atmospheric SciencesDeterministic Nonperiodic Flow
19,337 Citations1963Edward N. Lorenz
Physica D Nonlinear PhenomenaDetermining Lyapunov exponents from a time series
9,368 Citations1985Alan Wolf, J. B. Swift +2 more
Physical Review LettersMeasuring Information Transfer
4,535 Citations2000Thomas Schreiber
An information theoretic measure is derived that quantifies the statistical coherence between systems evolving in time and is able to distinguish effectively driving and responding elements and to detect asymmetry in the interaction of subsystems.
Europhysics Letters (EPL)Recurrence Plots of Dynamical Systems
3,272 Citations1987Jean‐Pierre Eckmann, Sylvie Oliffson Kamphorst +1 more
Reviews of Modern PhysicsThe analysis of observed chaotic data in physical systems
1,856 Citations1993Henry D. I. Abarbanel, Reggie Brown +2 more
Journal of Applied PhysiologyDynamical assessment of physiological systems and states using recurrence plot strategies
1,421 Citations1994C. L. Webber, Joseph P. Zbilut
This paper illustrates how recurrence plots can take single physiological measurements, project them into multidimensional space by embedding procedures, and identify time correlations (recurrences) that are not apparent in the one-dimensional time series.
Physics Letters AEmbeddings and delays as derived from quantification of recurrence plots
1,076 Citations1992Joseph P. Zbilut, Charles L. Webber
Recurrence plots have been advocated as a useful diagnostic tool for the assessment of dynamical time series by quantifying certain features of these plots which may be helpful in determining embeddings and delays.
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsRecurrence-plot-based measures of complexity and their application to heart-rate-variability data
989 Citations2002Norbert Marwan, Niels Wessel +3 more
Physics Letters ARecurrence quantification analysis of the logistic equation with transients
440 Citations1996Lluis Lligoña Trulla, Alessandro Giuliani +2 more
Physics Letters ADetecting deterministic signals in exceptionally noisy environments using cross-recurrence quantification
317 Citations1998Joseph P. Zbilut, Alessandro Giuliani +1 more
The proposed technique, cross-recurrence quantification, demonstrates the ability to extract signals up to a very low signal-to-noise-ratio and to allow an immediate appreciation of their degree of periodicity.
Nonlinear processes in geophysicsCross recurrence plot based synchronization of time series
267 Citations2002Norbert Marwan, Marko Thiel +1 more
Computer Methods in Applied Mechanics and EngineeringAn exploration of chaos
196 Citations1994F.H. Busse
Physica D Nonlinear PhenomenaAn attractor in a solar time series
181 Citations1987Jürgen Kurths, Hanspeter Herzel
Earth and Planetary Science LettersClimate change and mass movements in the NW Argentine Andes
116 Citations2000Martin H. Trauth, Ricardo N. Alonso +3 more
Journal of the Atmospheric SciencesStability of Jets in a Divergent Barotropic Fluid
58 Citations1963Frank B. Lipps
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsMeasuring statistical dependence and coupling of subsystems
46 Citations2000Andreas Schmitz
It is demonstrated that it is indeed possible to obtain nontrivial directional information, but it is also argued that the interpretation of this information is difficult.
Physics Letters ADivergence in perpendicular recurrence plot; quantification of dynamical divergence from short chaotic time series
40 Citations1999Jung-Mi Choi, BH Bae +1 more
A new toolkit, divergence in perpendicular recurrence plot (DPRP), which can roughly reflect the largest Lyapunov exponent (LLE), is proposed to consider a dynamical divergence of attractor reconstructed from very short time series.
Use of recurrence plots in analysis of time-series data
30 Citations1992M. Koebbe
Geometrical properties of the authors' plots provide dimensional complexity and local rate of divergence estimates and Eckmann, Kamphorst and Ruelle's idea of a recurrence plot, which they say helps appreciate the dynamics of a time series without either of these constraints.