Regensburg 2016 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 30: Poster - Complex nonlinear systems

DY 30.4: Poster

Dienstag, 8. März 2016, 18:15–21:00, Poster C

A novel measure to distinguish limit cycles and chaotic attractors — •Hendrik Wernecke, Bulcsú Sándor, and Claudius Gros — Institut für Theoretische Physik, Goethe-Universität Frankfurt am Main, Germany

In many dissipative dynamical systems exhibiting chaos there are parameter regions, where it is hard to distinguish between regular and chaotic motion. Then the attractors do not 'fill-up' the phase space, but the motion is bound to narrow areas. Furthermore, the maximum Lyapunov exponent can become arbitrary small in these regions, so that the standard classification can be difficult to interpret.

In the present work we describe a novel method that is able to draw a discrete distinction between limit cycles and chaotic attractors. Therefore we use the long-term distance between two trajectories starting close-by in the vicinity of the attractor and how this distance scales with the initial distance of trajectories. For the regular motion of a limit cycle one finds a linear scaling, while for the chaotic attractor the long-term distance is only correlated to the size of the attractor and therefore constant.

Furthermore, we propose a new classification of chaotic states in dissipative systems. We introduce the term 'weak dissipative chaos' for those chaotic attractors that can be distinguished from others by there topology. This classification is also indicated by the order of magnitude of the maximum Lyapunov exponent.