PT - JOURNAL ARTICLE
AU - Tyloo, M.
AU - Pagnier, L.
AU - Jacquod, P.
TI - The key player problem in complex oscillator networks and electric power grids: Resistance centralities identify local vulnerabilities
AID - 10.1126/sciadv.aaw8359
DP - 2019 Nov 01
TA - Science Advances
PG - eaaw8359
VI - 5
IP - 11
4099 - http://advances.sciencemag.org/content/5/11/eaaw8359.short
4100 - http://advances.sciencemag.org/content/5/11/eaaw8359.full
SO - Sci Adv2019 Nov 01; 5
AB - Identifying key players in coupled individual systems is a fundamental problem in network theory. We investigate synchronizable network-coupled dynamical systems such as high-voltage electric power grids and coupled oscillators on complex networks. We define key players as nodes that, once perturbed, generate the largest excursion away from synchrony. A spectral decomposition of the coupling matrix gives an elegant solution to this identification problem. We show that, when the coupling matrix is Laplacian, key players are peripheral in the sense of a centrality measure defined from effective resistance distances. For linearly coupled systems, the ranking is efficiently obtained through a single Laplacian matrix inversion, regardless of the operational synchronous state. The resulting ranking index is termed LRank. When nonlinearities are present, a weighted Laplacian matrix inversion gives another ranking index, WLRank. LRank provides a faithful ranking even for well-developed nonlinearities, corresponding to oscillator angle differences up to approximately Δθ ≲ 40°.