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.


Keywords:
Article Type:
scientifique
Faculty:
Ingénierie et Architecture
School:
HEI-VS
Institute:
Institut Systèmes industriels
Subject(s):
Ingénierie
Date:
2018
Pagination:
18 pages
Published in:
Physical review letters
Numeration (vol. no.):
2018, 120, 8
DOI:
ISSN:
0031-9007
External resources:
Appears in Collection:



 Record created 2018-07-10, last modified 2018-12-20

Fulltext:
Download fulltext
PDF

Rate this document:

Rate this document:
1
2
3
 
(Not yet reviewed)