2018
DOI: 10.1109/tcns.2017.2732161
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Self-Organization of Weighted Networks for Optimal Synchronizability

Abstract: We show that a network can self-organize its structure in a completely distributed manner in order to optimize its synchronizability whilst satisfying the local constraints: non-negativity of edge weights, and maximum weighted degree of nodes. A novel multilayer approach is presented which uses a distributed strategy to estimate two spectral functions of the graph Laplacian, the algebraic connectivity λ2 and the eigenratio r = λn/λ2. These local estimates are then used to evolve the edge weights so as to maxim… Show more

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Cited by 24 publications
(12 citation statements)
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“…two network-dependent measures able to capture the synchronizability of a network of identical coupled oscillators. Based on this connection, we find in the literature several works aiming to optimize the synchronizability of a network of identical coupled oscillators using the Laplacian matrix (Pecora and Carroll, 1998;Nishikawa and Motter, 2006;Donetti et al, 2005;Rad et al, 2008;Motter et al, 2005Motter et al, , 2013Kempton et al, 2015;Skardal and Arenas, 2015;Fardad et al, 2014a;Clark et al, 2014;Mousavi et al, 2016;Siami and Motee, 2016).…”
mentioning
confidence: 99%
“…two network-dependent measures able to capture the synchronizability of a network of identical coupled oscillators. Based on this connection, we find in the literature several works aiming to optimize the synchronizability of a network of identical coupled oscillators using the Laplacian matrix (Pecora and Carroll, 1998;Nishikawa and Motter, 2006;Donetti et al, 2005;Rad et al, 2008;Motter et al, 2005Motter et al, , 2013Kempton et al, 2015;Skardal and Arenas, 2015;Fardad et al, 2014a;Clark et al, 2014;Mousavi et al, 2016;Siami and Motee, 2016).…”
mentioning
confidence: 99%
“…Similarly, one could think of redistributing the link weights of a network, characterized by a given adjacency matrix, so as to ensure that a set of nodes is visited with some frequency in the resulting weighted network, or that no link carries more than a certain amount of some flow. While this problem is less intensively investigated than that of optimal paths, examples can be found in the literature of, e.g., networks that are optimal for sustaining a synchronized dynamics [19][20][21][22]. Recent contributions based on a kindred dynamical-control approach show how to engineer force fields in many-particle systems so as to achieve prescribed steady-state distributions [23][24][25].…”
Section: Introductionmentioning
confidence: 99%
“…However, in the above cases, the network topology of both the relay and remote layers are represented by unweighted networks. Although weighted networks, where coupling weights are heterogeneous, are present in many real-world networks, such as the network of scientific collaborations [39], structural and functional networks of the brain [40], transportation networks [41], epidemic spreading [42], ecological networks [43], etc., we would like to emphasize that the recent progress in this direction has been achieved considering weighted mono-layer networks [44][45][46][47][48] and weighted duplex networks [49][50][51]. However, the effect of weighted networks upon synchronization in the multiplex network with more than two layers is less studied.…”
Section: Introductionmentioning
confidence: 99%