Multivariate Recurrence Plots

M Carmen Romano , Marco Thiel, Jurgen Kurths, W. von Bloh

Research output: Contribution to journalArticlepeer-review

119 Citations (Scopus)


We propose a new approach to calculate recurrence plots of multivariate time series, based on joint recurrences in phase space. This new method allows to estimate dynamical invariants of the whole system, like the joint Renyi entropy of second order. We use this entropy measure to quantitatively study in detail the phase synchronization of two bidirectionally coupled chaotic systems and identify different types of transitions to chaotic phase synchronization in dependence on the coupling strength and the frequency mismatch. By means of this analysis we find several new phenomena, such a chaos-period-chaos transition to phase synchronization for rather large coupling strengths. (C) 2004 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)214-223
Number of pages10
JournalPhysics Letters A
Issue number3-4
Publication statusPublished - Sept 2004


  • coupled chaotic systems
  • phase synchronization
  • lag synchronization
  • time-series
  • oscillators
  • quantification


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