On the topology of synchrony optimized networks of a Kuramoto-model with non-identical oscillators
Kelly, David (David T. B.) and Gottwald, Georg A.. (2011) On the topology of synchrony optimized networks of a Kuramoto-model with non-identical oscillators. Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol.21 (No.2). Article no. 025110. ISSN 10541500Full text not available from this repository.
Official URL: http://dx.doi.org/10.1063/1.3590855
We study synchrony optimized networks. In particular, we focus on the Kuramoto model with non-identical native frequencies on a random graph. In a first step, we generate synchrony optimized networks using a dynamic breeding algorithm, whereby an initial network is successively rewired toward increased synchronization. These networks are characterized by a large anti-correlation between neighbouring frequencies. In a second step, the central part of our paper, we show that synchrony optimized networks can be generated much more cost efficiently by minimization of an energy-like quantity E and subsequent random rewires to control the average path length. We demonstrate that synchrony optimized networks are characterized by a balance between two opposing structural properties: A large number of links between positive and negative frequencies of equal magnitude and a small average path length. Remarkably, these networks show the same synchronization behaviour as those networks generated by the dynamic rewiring process. Interestingly, synchrony-optimized network also exhibit significantly enhanced synchronization behaviour for weak coupling, below the onset of global synchronization, with linear growth of the order parameter with increasing coupling strength. We identify the underlying dynamical and topological structures, which give rise to this atypical local synchronization, and provide a simple analytical argument for its explanation.
|Item Type:||Journal Article|
|Divisions:||Faculty of Science > Mathematics|
|Journal or Publication Title:||Chaos: An Interdisciplinary Journal of Nonlinear Science|
|Publisher:||American Institute of Physics|
|Page Range:||Article no. 025110|
|Access rights to Published version:||Restricted or Subscription Access|
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