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

Abstract

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.

Authors:
 [1];  [2]
  1. Facultad Politénica, UNA, Asunción (Paraguay)
  2. School of Engineering, UDELAR, Montevideo 11300 (Uruguay)
Publication Date:
OSTI Identifier:
22402532
Resource Type:
Journal Article
Resource Relation:
Journal Name: Chaos (Woodbury, N. Y.); Journal Volume: 25; Journal Issue: 2; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; EQUILIBRIUM; GRAPH THEORY; OSCILLATORS; STABILITY; SYNCHRONIZATION; WEAK-COUPLING MODEL

Citation Formats

Canale, Eduardo A., E-mail: ecanale@pol.una.py, and Monzón, Pablo, E-mail: monzon@fing.edu.uy. Exotic equilibria of Harary graphs and a new minimum degree lower bound for synchronization. United States: N. p., 2015. Web. doi:10.1063/1.4907952.
Canale, Eduardo A., E-mail: ecanale@pol.una.py, & Monzón, Pablo, E-mail: monzon@fing.edu.uy. Exotic equilibria of Harary graphs and a new minimum degree lower bound for synchronization. United States. doi:10.1063/1.4907952.
Canale, Eduardo A., E-mail: ecanale@pol.una.py, and Monzón, Pablo, E-mail: monzon@fing.edu.uy. Sun . "Exotic equilibria of Harary graphs and a new minimum degree lower bound for synchronization". United States. doi:10.1063/1.4907952.
@article{osti_22402532,
title = {Exotic equilibria of Harary graphs and a new minimum degree lower bound for synchronization},
author = {Canale, Eduardo A., E-mail: ecanale@pol.una.py and Monzón, Pablo, E-mail: monzon@fing.edu.uy},
abstractNote = {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.},
doi = {10.1063/1.4907952},
journal = {Chaos (Woodbury, N. Y.)},
number = 2,
volume = 25,
place = {United States},
year = {Sun Feb 15 00:00:00 EST 2015},
month = {Sun Feb 15 00:00:00 EST 2015}
}