Synchronization phenomena in systems with complicated topology

Jürgen Kurths,
Potsdam University

Synchronization of coupled complex oscillatory systems has been so far mostly studied for rather phase-coherent dynamics. This is a strong restriction for many applications. In this talk two new approaches to identify synchronization will be presented. The first one is based on the general idea of curvature of an arbitrary curve. The second one is using properties of recurrences of a system's trajectory in phase space. It will be shown that both methods are able to identify and quantify phase synchronization for ensembles of coupled Rössler systems in the funnel regime and also for coupled Type-I-Intermittency systems. Moreover, both allow to distinguish phase from generalized synchronization. The second method is applicable even for noisy data. Finally, experimental data from electrochemical oscillators will be analysed.