Dresden 2011 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 10: Posters I

DY 10.28: Poster

Montag, 14. März 2011, 17:00–19:00, P4

Determination of the attractor dimension at the synchronization transition of a delayed chaotic system — •Steffen Zeeb and Wolfgang Kinzel — Institut für Theoretische Physik, Universität Würzburg

A network of nonlinear units interacting by time-delayed couplings can sychronize to a common chaotic trajectory. Although the transmission time may be very long the units are completely synchronized without time shift.

We investigate the transition to synchronization. In particular, for networks of iterated maps we determine the Kaplan-Yorke dimension from the spectra of Lyapunov exponents which are calculated analytically for Bernoulli maps and numerically for tent maps. However, we argue that the Kaplan-Yorke conjecture cannot be true at the transition. For the synchronized state the Lyapunov exponents perpendicular to the synchronization manifold cannot contribute to the attractor dimension. Consequently, the attractor dimension has to jump discontinuously at the transition. We calculate the magnitude of this jump for different networks.

Finally, the Kaplan-Yorke dimension is compared to the information and correlation dimension, respectively, in order to check the discontinuous behavior of the attractor dimension.