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Optimal synchronization of complex networks
Per Sebastian Skardal1, Dane Taylor2, Jie Sun3
1Departament d'Enginyeria Informatica i Matemátiques, Universitat Rovira i Virgili, 43007 Tarragona, Spain and Department of Applied Mathematics, University of Colorado at Boulder, Boulder, Colorado 80309, USA.
Abstract:
We study optimal synchronization in networks of heterogeneous phase oscillators. Our main result is the derivation of a synchrony alignment function that encodes the interplay between network structure and oscillators' frequencies and that can be readily optimized. We highlight its utility in two general problems: constrained frequency allocation and network design. In general, we find that synchronization is promoted by strong alignments between frequencies and the dominant Laplacian eigenvectors, as well as a matching between the heterogeneity of frequencies and network structure.
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