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DY: Fachverband Dynamik und Statistische Physik

DY 33: Poster II

DY 33.51: Poster

Donnerstag, 14. März 2013, 17:00–19:00, Poster C

Scaling properties and synchronisation in chaotic networks with multiple delays — •Otti D'Huys¹, Steffen Zeeb¹, Sven Heiligenthal¹, Thomas Juengling¹, Wolfgang Kinzel¹, and Serhiy Yanchuk² — ¹Institute of Theoretical Physics, University of Wuerzburg, 97074 Wuerzburg, Germany — ²Institute of Mathematics, Humboldt University of Berlin, 10099 Berlin, Germany

Delayed complex systems have received much interest in recent years, as delays play an important role in systems as diverse as population dynamics, traffic, communication networks, genetic circuits, and the brain. In general the different interaction delays in a network are not equal, or may even differ by several orders of magnitude.

We consider a hierarchical network of chaotic units: the coupling delay within a subnetwork is much shorter than the delay between the subnetworks. We show that the spectrum of Lyapunov exponents has a typical structure, with different parts of the spectrum scaling with the different delays. We can relate the scaling properties of the maximal Lyapunov exponent to the synchronisation properties of the network: units within a subnetwork can synchronise if the maximal exponent scales with the shorter delay while long range synchronisation between different subnetworks is only possible if the maximal exponent scales with the long delay.