Regensburg 2004 – scientific programme

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DY: Dynamik und Statistische Physik

DY 21: Neural Networks

DY 21.3: Talk

Tuesday, March 9, 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).