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DY: Fachverband Dynamik und Statistische Physik

DY 59: Posters - Nonlinear General

DY 59.1: Poster

Donnerstag, 23. März 2017, 17:00–19:30, P1A

Tests for chaos and partial predictability — •Hendrik Wernecke, Bulcsú Sándor, and Claudius Gros — Goethe-Universität Frankfurt am Main, Institut für Theoretische Physik, Max-von-Laue-Straße 1, 60438 Frankfurt am Main

For deterministic dynamical systems the exponential divergence of pairs of initially close trajectories on the attracting set is a tell-tale indicator for chaos. This process can lead to a total loss of correlation within the time scale of the Lyapunov prediction time. However, there is a type of chaotic motion, for which the time scale of decorrelation is dominantly determined by a diffusive process on the attractor. This type of chaos stays partially predictable for remarkably long time. However, due to the high level of cross-correlation, the standard tests for chaos either yield ambiguous results or misclassify partially predictable chaos as laminar flow. Therefore we present in this study a novel indicator for chaos based on the cross-distance scaling of pairs of initially close trajectories. This test is capable of robustly and unambiguously distinguishing chaotic dynamics, including partially predictable chaos, from laminar flow in a 0-1 fashion. In combination with the finite-time cross-correlation, we are able to distinguish all three types of motion -- chaos, partially predictable chaos and laminar flow -- in a 0-1 manner from the time evolution of pairs of trajectories.