Abstract:
: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°.
journal_name
Sci Advjournal_title
Science advancesauthors
Tyloo M,Pagnier L,Jacquod Pdoi
10.1126/sciadv.aaw8359subject
Has Abstractpub_date
2019-11-22 00:00:00pages
eaaw8359issue
11issn
2375-2548pii
aaw8359journal_volume
5pub_type
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