Regensburg 2010 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 30: Posters II
DY 30.24: Poster
Donnerstag, 25. März 2010, 16:00–18:00, Poster C
Identifying shrimp structures in continuous dynamical systems using recurrence-based methods — Yong Zou1, •Reik V. Donner1,2,3, Jonathan F. Donges1,4, Norbert Marwan1, and Jürgen Kurths1,4 — 1Potsdam Institute for Climate Impact Research, Potsdam, Germany — 2Max Planck Institute for Physics of Complex Systems, Dresden, Germany — 3Institute for Transport and Economics, Dresden University of Technology, Germany — 4Department of Physics, Humboldt University of Berlin, Germany
The identification of some specific periodic islands (so-called shrimps) in the two-dimensional parameter space of certain complex systems has recently attracted considerable interest. While for discrete systems, a discrimination between periodic and chaotic windows can be easily made based on the maximum Lyapunov exponent of the system, this is a challenging task for continuous systems, especially if only short time series are available (e.g., in case of experimental data). In this work, we demonstrate that nonlinear measures based on recurrence plots obtained from such trajectories provide a practicable alternative for numerically detecting shrimps. Traditional diagonal line-based measures of recurrence quantification analysis (RQA) as well as measures from complex network theory are shown to allow a reasonable classification of periodic and chaotic behavior in parameter space. Average path length and clustering coefficient of the resulting recurrence networks are found to be particularly powerful discriminatory statistics for the identification of shrimps in the Rössler system.