Dresden 2011 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 26: Nonlinear Dynamics II

DY 26.4: Vortrag

Mittwoch, 16. März 2011, 17:15–17:30, ZEU 255

The Geometry of Chaotic Dynamics - A Complex Network Perspective — •Reik V. Donner¹, Jobst Heitzig¹, Jonathan F. Donges^1,2, Yong Zou¹, Norbert Marwan¹, and Jürgen Kurths^1,2 — ¹Potsdam Institute for Climate Impact Research, Potsdam, Germany — ²Department of Physics, Humboldt University of Berlin, Germany

Among the different existing complex network approaches to time series analysis, ε-recurrence networks most faithfully represent the geometrical fine structure of the underlying chaotic attractors. We demonstrate that the well known graph theoretical properties local clustering coefficient and global network transitivity can meaningfully be exploited to define new local and global measures of dimension in phase space. Rigorous analytical as well as numerical results for self-similar sets and simple chaotic model systems suggest that these measures are well-behaved in most non-pathological situations and that they can be estimated reasonably well using ε-recurrence networks constructed from relatively short time series. These findings theoretically explain why the networks’ transitivity properties are particularly well suited for identifying dynamically invariant objects as well as regime shifts in non-stationary time series. Our results demonstrate that ε-recurrence networks exhibit an important link between dynamical systems and graph theory.