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

Eduardo A. Canale; Pablo Monzón

doi:10.1063/1.4907952

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

Eduardo A. Canale, Pablo Monzón

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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 language	English (US)
Pages (from-to)	023106
Journal	Chaos: An Interdisciplinary Journal of Nonlinear Science
Volume	25
Issue number	2
DOIs	https://doi.org/10.1063/1.4907952
State	Published - Feb 2015
Externally published	Yes

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title = "Exotic equilibria of Harary graphs and a new minimum degree lower bound for synchronization",

abstract = "{\textcopyright} 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.",

author = "Canale, {Eduardo A.} and Pablo Monz{\'o}n",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: This work was partially done during the scientific visit of the first author to the team of Ra{\'u}l Tempone at KAUST (King Abdullah University of Science and Technology). We want to thank the anonymous referees for their useful comments and suggestions. This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

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AU - Monzón, Pablo

N1 - KAUST Repository Item: Exported on 2020-10-01 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. This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2015/2

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N2 - © 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.

AB - © 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.

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

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