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Preprint
The Kuramoto model on power law graphs
arXiv.org
13 May 2017
Abstract
The Kuramoto model (KM) of coupled phase oscillators on scale free graphs is
analyzed in this work. The W-random graph model is used to define a convergent
family of sparse graphs with power law degree distribution. For the KM on this
family of graphs, we derive the mean field description of the system's dynamics
in the limit as the size of the network tends to infinity. The mean field
equation is used to study two problems: synchronization in the coupled system
with randomly distributed intrinsic frequencies and existence and bifurcations
of chimera states in the KM with repulsive coupling. The analysis of both
problems highlights the role of the scale free network organization in shaping
dynamics of the coupled system. The analytical results are complemented with
the results of numerical simulations.
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Details
- Title
- The Kuramoto model on power law graphs
- Creators
- Georgi S MedvedevXuezhi Tang
- Publication Details
- arXiv.org
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Mathematics
- Other Identifier
- 991021862731004721