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Berlin 2012 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 10: Nonlinear Dynamics, Synchronisation and Chaos

DY 10.11: Vortrag

Dienstag, 27. März 2012, 12:15–12:30, MA 001

Onset of Synchronization in Complex Networks of Noisy Oscillators — •Bernard Sonnenschein1,2 and Lutz Schimansky-Geier1,21Institute of Physics, Humboldt University at Berlin, Newtonstr. 15, 12489 Berlin, Germany — 2Bernstein Center for Computational Neuroscience, Philippstr. 13, 10115 Berlin, Germany

We investigate noisy Kuramoto oscillators on networks that are undirected and complex. Our problem allows to study the effects and the interplay of networks with a given degree distribution, diversity of oscillators and noise acting on the natural frequencies.

We derive the critical coupling strength for the onset of synchronization by approximating the complex network by a weighted fully connected network.

We find that the critical coupling strength is a product of two factors. The first one depends solely on the network topology, while the second factor is a function of the noise intensity and the diversity of the oscillators. Our result is applied to a dense small-world network model in order to provide numerical verification.

We obtain a satisfying agreement between simulations and theory for the critical coupling strength, regardless of whether we consider the dependencies on the topology or the dependencies on the diversity.

Only for a smaller number of edges in the network, the critical coupling strength is slightly overestimated by our approximation technique, but the functional dependencies can still be reproduced qualitatively.

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