# 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:

- Facultad Politénica, UNA, Asunción (Paraguay)
- 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}

}

DOI: 10.1063/1.4907952

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