University of Potsdam, Potsdam, Germany

In the classical sense, synchronization of coupled oscillating systems means appearance of certain relations between their phases and frequencies due to weak coupling. After giving brief introduction into the classical theory we review its recent extension to the case of chaotic systems. We discuss how the phase and mean frequency can be determined and consider synchronization effects in two- or many-oscillator systems.

Next, we discuss how synchronization theory can be used in data analysis. In particular, we consider how the phases and frequencies can be estimated from time series and how the intensity and directionality of interaction can be estimated. The methods are illustrated by the results of the investigation of cardiorespiratory interaction in humans.

**References**

Pikovsky A, Rosenblum M and Kurths J 2001
*Synchronization: A Universal Concept in Nonlinear Sciences*
(Cambridge: Cambridge University Press)

Rosenblum M *et al* 2001 in *Handbook of Biological Physics*
eds. F. Moss and S. Gielen (Amsterdam: North-Holland) vol4, pp279-321

Pikovsky A, Rosenblum M and Kurths J 2001
*Int. J. of Bifurcation and Chaos* **10** pp2291-2306.