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

Eduardo A. Canale, Pablo Monzón

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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.
Original languageEnglish (US)
Pages (from-to)023106
JournalChaos: An Interdisciplinary Journal of Nonlinear Science
Volume25
Issue number2
DOIs
StatePublished - Feb 2015
Externally publishedYes

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