### Résumé

There is recent evidence that the XY spin model on complex networks can display three different macroscopic states in response to the topology of the network underpinning the interactions of the spins. In this work we present a way to characterize the macroscopic states of the XY spin model based on the spectral decomposition of time series using topological information about the underlying networks. We use three different classes of networks to generate time series of the spins for the three possible macroscopic states. We then use the temporal Graph Signal Transform technique to decompose the time series of the spins on the eigenbasis of the Laplacian. From this decomposition, we produce spatial power spectra, which summarize the activation of structural modes by the nonlinear dynamics, and thus coherent patterns of activity of the spins. These signatures of the macroscopic states are independent of the underlying network class and can thus be used as robust signatures for the macroscopic states. This work opens avenues to analyze and characterize dynamics on complex networks using temporal Graph Signal Analysis.

langue | Anglais |
---|---|

Numéro d'article | 012312 |

journal | Physical Review E |

Volume | 96 |

Numéro | 1 |

Les DOIs | |

état | Publié - 11 juil. 2017 |

### Empreinte digitale

### Citer ceci

*Physical Review E*,

*96*(1), [012312]. DOI: 10.1103/PhysRevE.96.012312

}

*Physical Review E*, VOL. 96, Numéro 1, 012312. DOI: 10.1103/PhysRevE.96.012312

**Graph spectral characterization of the XY model on complex networks.** / Expert, Paul; De Nigris, Sarah; Takaguchi, Taro; Lambiotte, Renaud.

Résultats de recherche: Contribution à un journal/une revue › Article

TY - JOUR

T1 - Graph spectral characterization of the XY model on complex networks

AU - Expert,Paul

AU - De Nigris,Sarah

AU - Takaguchi,Taro

AU - Lambiotte,Renaud

PY - 2017/7/11

Y1 - 2017/7/11

N2 - There is recent evidence that the XY spin model on complex networks can display three different macroscopic states in response to the topology of the network underpinning the interactions of the spins. In this work we present a way to characterize the macroscopic states of the XY spin model based on the spectral decomposition of time series using topological information about the underlying networks. We use three different classes of networks to generate time series of the spins for the three possible macroscopic states. We then use the temporal Graph Signal Transform technique to decompose the time series of the spins on the eigenbasis of the Laplacian. From this decomposition, we produce spatial power spectra, which summarize the activation of structural modes by the nonlinear dynamics, and thus coherent patterns of activity of the spins. These signatures of the macroscopic states are independent of the underlying network class and can thus be used as robust signatures for the macroscopic states. This work opens avenues to analyze and characterize dynamics on complex networks using temporal Graph Signal Analysis.

AB - There is recent evidence that the XY spin model on complex networks can display three different macroscopic states in response to the topology of the network underpinning the interactions of the spins. In this work we present a way to characterize the macroscopic states of the XY spin model based on the spectral decomposition of time series using topological information about the underlying networks. We use three different classes of networks to generate time series of the spins for the three possible macroscopic states. We then use the temporal Graph Signal Transform technique to decompose the time series of the spins on the eigenbasis of the Laplacian. From this decomposition, we produce spatial power spectra, which summarize the activation of structural modes by the nonlinear dynamics, and thus coherent patterns of activity of the spins. These signatures of the macroscopic states are independent of the underlying network class and can thus be used as robust signatures for the macroscopic states. This work opens avenues to analyze and characterize dynamics on complex networks using temporal Graph Signal Analysis.

UR - http://www.scopus.com/inward/record.url?scp=85026435468&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.96.012312

DO - 10.1103/PhysRevE.96.012312

M3 - Article

VL - 96

JO - Physical Review E

T2 - Physical Review E

JF - Physical Review E

SN - 1539-3755

IS - 1

M1 - 012312

ER -