Exotic equilibria of Harary graphs and a new minimum degree lower bound for synchronization

Type
Article

Authors
Canale, Eduardo A.
Monzón, Pablo

Date
2015-02

Abstract
© 2015 AIP Publishing LLC. This work is concerned with stability of equilibria in the homogeneous (equal frequencies) Kuramoto model of weakly coupled oscillators. In 2012 [R. Taylor, J. Phys. A: Math. Theor. 45, 1-15 (2012)], a sufficient condition for almost global synchronization was found in terms of the minimum degree-order ratio of the graph. In this work, a new lower bound for this ratio is given. The improvement is achieved by a concrete infinite sequence of regular graphs. Besides, non standard unstable equilibria of the graphs studied in Wiley et al. [Chaos 16, 015103 (2006)] are shown to exist as conjectured in that work.

Citation
Canale EA, Monzón P (2015) Exotic equilibria of Harary graphs and a new minimum degree lower bound for synchronization. Chaos: An Interdisciplinary Journal of Nonlinear Science 25: 023106. Available: http://dx.doi.org/10.1063/1.4907952.

Acknowledgements
This work was partially done during the scientific visit of the first author to the team of Raúl Tempone at KAUST (King Abdullah University of Science and Technology). We want to thank the anonymous referees for their useful comments and suggestions.

Publisher
AIP Publishing

Journal
Chaos: An Interdisciplinary Journal of Nonlinear Science

DOI
10.1063/1.4907952

PubMed ID
25725642

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