Robustness of synchrony in complex networks and generalized Kirchhoff indices

Tyloo, Melvyn (School of Engineering, HES-SO Valais-Wallis, HEI, HES-SO // University of Applied Sciences Western Switzerland ; Institute of Physics, EPF Lausanne, CH-1015 Lausanne, Switzerland) ; Coletta, Tommaso (School of Engineering, HES-SO Valais-Wallis, HEI, HES-SO // University of Applied Sciences Western Switzerland) ; Jacquod, Philippe (School of Engineering, HES-SO Valais-Wallis, HEI, HES-SO // University of Applied Sciences Western Switzerland)

In network theory, a question of prime importance is how to assess network vulnerability in a fast and reliable manner. With this issue in mind, we investigate the response to external perturbations of coupled dynamical systems on complex networks. We find that for specific, nonaveraged perturbations, the response of synchronous states depends on the eigenvalues of the stability matrix of the unperturbed dynamics, as well as on its eigenmodes via their overlap with the perturbation vector. Once averaged over properly defined ensembles of perturbations, the response is given by new graph topological indices, which we introduce as generalized Kirchhoff indices. These findings allow for a fast and reliable method for assessing the specific or average vulnerability of a network against changing operational conditions, faults, or external attacks.


Mots-clés:
Type d'article:
scientifique
Faculté:
Ingénierie et Architecture
Ecole:
HEI-VS
Institut:
Institut Systèmes industriels
Classification:
Ingénierie
Date:
2018
Pagination:
18 pages
Publié dans
Physical review letters
Numérotation (vol. no.):
2018, 120, 8
DOI:
ISSN:
0031-9007
Ressource(s) externe(s):
Le document apparaît dans:



 Notice créée le 2018-07-10, modifiée le 2018-12-11

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