M. Carmen Romano^a, Marco Thiel^a, Jürgen Kurths^a and Werner von Bloh^b

Physics Letters A 330 (3-4), 214-223 (2004)

^aUniversity of Potsdam, Nonlinear Dynamics, Am Neuen Palais 10, 14469 Potsdam, Germany.

^bPotsdam Institute for Climate Impact Research (PIK), Telegrafenberg, P.O. Box 60 12 03, 14412 Potsdam, Germany.

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.