Global robustness versus local vulnerabilities in complex synchronous networks

Tyloo, Melvyn Sandy (Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland ; School of Engineering, HES-SO Valais-Wallis, HEI, HES-SO // University of Applied Sciences Western Switzerland) ; Jacquod, Philippe (Department of Quantum Matter Physics, university of Geneva, Geneva, Switzerland ; School of Engineering, HES-SO Valais-Wallis, HEI, HES-SO // University of Applied Sciences Western Switzerland)

In complex network-coupled dynamical systems, two questions of central importance are how to identify the most vulnerable components and how to devise a network making the overall system more robust to external perturbations. To address these two questions, we investigate the response of complex networks of coupled oscillators to local perturbations. We quantify the magnitude of the resulting excursion away from the unperturbed synchronous state through quadratic performance measures in the angle or frequency deviations. We find that the most fragile oscillators in a given network are identified by centralities constructed from network resistance distances. Further defining the global robustness of the system from the average response over ensembles of homogeneously distributed perturbations, we find that it is given by a family of topological indices known as generalized Kirchhoff indices. Both resistance centralities and Kirchhoff indices are obtained from a spectral decomposition of the stability matrix of the unperturbed dynamics and can be expressed in terms of resistance distances. We investigate the properties of these topological indices in small-world and regular networks. In the case of oscillators with homogeneous inertia and damping coefficients, we find that inertia only has small effects on robustness of coupled oscillators. Numerical results illustrate the validity of the theory.


Keywords:
Article Type:
scientifique
Faculty:
Ingénierie et Architecture
School:
HEI-VS
Institute:
Institut Énergie et environnement
Date:
2019-09
Pagination:
11 p.
Published in:
Physical Review E
Numeration (vol. no.):
2019, vol. 100, no. 3, article no. 032303
DOI:
ISSN:
2470-0045
Appears in Collection:



 Record created 2020-01-24, last modified 2020-01-24

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