Regensburg 2010 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 10: Nonlinear Dynamics I

DY 10.7: Vortrag

Dienstag, 23. März 2010, 15:30–15:45, H46

Recurrence networks: A novel paradigm for nonlinear time series analysis — •Reik V. Donner^1,2,3, Yong Zou³, Jonathan F. Donges^3,4, Norbert Marwan³, and Jürgen Kurths^3,4 — ¹Max Planck Institute for Physics of Complex Systems, Dresden, Germany — ²Institute for Transport and Economics, Dresden University of Technology, Germany — ³Potsdam Institute for Climate Impact Research, Potsdam, Germany — ⁴Department of Physics, Humboldt University of Berlin, Germany

We present a novel approach for analysing structural properties of dynamical systems based on time series. Starting from the concept of recurrences in phase space, the recurrence matrix of a time series is interpreted as the adjacency matrix of an associated complex network which links different points in time if the evolution of the considered states is very similar. A critical comparison of these recurrence networks with similar existing techniques is presented, revealing strong conceptual benefits of the new approach which can be considered as a unifying framework for transforming time series into complex networks that also includes other methods as special cases.

We demonstrate the presence of fundamental relationships between the topological properties of recurrence networks and the statistical properties of the phase space density of the underlying dynamical system. Hence, the network description yields new quantitative characteristics of the dynamical complexity of a time series, which substantially complement existing measures of recurrence quantification analysis.