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DY: Dynamik und Statistische Physik
DY 21: Neural Networks
DY 21.3: Vortrag
Dienstag, 9. März 2004, 10:45–11:00, H3
Topological Speed Limits to Network Synchronization — •Marc Timme, Fred Wolf, and Theo Geisel — Max-Planck-Institut für Strömungsforschung, Bunsenstr. 10, 37073 Göttingen
Pulse-coupled oscillators constitute a paradigmatic class of dynamical
systems interacting on networks because they model a variety of biological
systems including flashing fireflies and chirping crickets as well as
pacemaker cells of the heart and neural networks. Synchronization is one of
the most simple and most prevailing kinds of collective dynamics on such
networks.
Here we study collective synchronization of pulse-coupled oscillators
interacting on asymmetric random networks. Using random matrix theory we
accurately predict the speed of synchronization in such networks in
dependence on the dynamical and network parameters [1]. As might be
expected, the speed of synchronization increases with increasing coupling
strengths. Surprisingly, however, it stays finite even for infinitely
strong interactions. Our results indicate that the speed of synchronization
is limited by the connectivity of the network.
[1] M. Timme, F. Wolf, and T. Geisel, cond-mat/0306512 (2003).