Multivariate recurrence plots

Romano, M. C.; Thiel, M.; Kurths, Jürgen; von Bloh, Werner

doi:10.1016/j.physleta.2004.07.066

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Multivariate recurrence plots

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Romano, M. C.
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Thiel, M.
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/persons/resource/Juergen.Kurths

Kurths, Jürgen
Potsdam Institute for Climate Impact Research;

/persons/resource/Werner.von.Bloh

von Bloh, Werner
Potsdam Institute for Climate Impact Research;

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Romano, M. C., Thiel, M., Kurths, J., von Bloh, W. (2004): Multivariate recurrence plots. - Physics Letters A, 330, 3-4, 214-223.
https://doi.org/10.1016/j.physleta.2004.07.066

Cite as: https://publications.pik-potsdam.de/pubman/item/item_12387

Abstract

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 Rényi 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.