title: Optimal synchronization of complex networks.
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.
authors.affiliation: Departament 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.
authors.forename: Per Sebastian
authors.initials: PS
authors.lastname: Skardal
authors.affiliation: Department of Applied Mathematics, University of Colorado at Boulder, Boulder, Colorado 80309, USA and Statistical and Applied Mathematical Sciences Institute, Research Triangle Park, North Carolina 27709, USA and Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina 27599, USA.
authors.forename: Dane
authors.initials: D
authors.lastname: Taylor
authors.affiliation: Department of Mathematics, Clarkson University, Potsdam, New York 13699, USA.
authors.forename: Jie
authors.initials: J
authors.lastname: Sun