Summary

Proceedings of the 2012 International Symposium on Nonlinear Theory and its Applications

2012

Session Number:A3L-B

Session:

Number:171

Synchronization of Kuramoto oscillators in networks of networks

Per Sebastian Skardal,  Juan G. Restrepo,  

pp.171-174

Publication Date:

Online ISSN:2188-5079

DOI:10.15248/proc.1.171

PDF download (351.3KB)

We study synchronization of Kuramoto oscillators in strongly modular networks in which the structure of the network inside each community is averaged. We find that the dynamics of the interacting communities can be described as an ensemble of coupled planar oscillators. In the limit of a large number of communities, we find a low dimensional description of the level of synchronization between the communities. In this limit, we describe bifurcations between incoherence, local synchrony, and global synchrony. We compare the predictions of this simplified model with simulations of heterogeneous networks in which the internal structure of each community is preserved and find excellent agreement. Finally, we investigate synchronization in networks where several layers of communities within communities may be present.

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