Self-Organization of Weighted Networks for Optimal Synchronizability
Louis Kempton, Guido Herrmann, Mario di Bernardo · IEEE Transactions on Control of Network Systems · 2017
We show that a network can self-organize its existing topology, i.e., by adapting edge weights, in a completely decentralized manner in order to maximize its synchronizability while satisfying local constraints: we look specifically at nonnegativity of edge weights and maximum weighted degree of nodes. A novel multilayer approach is presented, which uses a decentralized strategy through which each node can estimate one of two spectral functions of the graph Laplacian, the algebraic connectivity λ2, or the eigenratio r = λn/λ2. These local estimates are then used to evolve the edge weights so as to maximize λ2, or minimizer, and, hence, achieve globally optimal values for the edge weights for the synchronization of a network of coupled systems.