Nonlinear analysis of bivariate data with cross recurrence plots

2002/01/31 by Norbert Marwan, N. Marwan, Jürgen Kurths +1 · 6 citations
Computer Science · Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Chaos control and synchronization #Complex Systems and Time Series Analysis #Nonlinear Dynamics and Pattern Formation #math-ph #math.MP #nlin.CD #physics.data-an #physics.geo-ph

paper · pdf · doi:10.1016/s0375-9601(02)01170-2

published as Physics Letters A, 302(5-6), 2002, 299-307

arxiv created 2002/08/16 · openalex publication_date 2002/09/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• <i>The Fractal Geometry of Nature</i>
• Deterministic Nonperiodic Flow
• Determining Lyapunov exponents from a time series

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