title: Synchronization in dynamical networks with unconstrained structure switching.
abstract: We provide a rigorous solution to the problem of constructing a structural evolution for a network of coupled identical dynamical units that switches between specified topologies without constraints on their structure. The evolution of the structure is determined indirectly from a carefully built transformation of the eigenvector matrices of the coupling Laplacians, which are guaranteed to change smoothly in time. In turn, this allows one to extend the master stability function formalism, which can be used to assess the stability of a synchronized state. This approach is independent from the particular topologies that the network visits, and is not restricted to commuting structures. Also, it does not depend on the time scale of the evolution, which can be faster than, comparable to, or even secular with respect to the dynamics of the units.
authors.affiliation: School of Life Sciences, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, United Kingdom.|Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, D-01187 Dresden, Germany.
authors.forename: Charo I
authors.initials: CI
authors.lastname: del Genio
authors.affiliation: Departamento de Matématica Aplicada, Universidad Rey Juan Carlos, 28933 Móstoles, Madrid, Spain.|Center for Biomedical Technology, Universidad Politécnica de Madrid, 28223 Pozuelo de Alarcón, Madrid, Spain.
authors.forename: Miguel
authors.initials: M
authors.lastname: Romance
authors.affiliation: Departamento de Matématica Aplicada, Universidad Rey Juan Carlos, 28933 Móstoles, Madrid, Spain.|Center for Biomedical Technology, Universidad Politécnica de Madrid, 28223 Pozuelo de Alarcón, Madrid, Spain.
authors.forename: Regino
authors.initials: R
authors.lastname: Criado
authors.affiliation: CNR-Institute of Complex Systems, Via Madonna del Prato, 10, 50019 Sesto Fiorentino (FI), Italy.|Embassy of Italy in Israel, Trade Tower, 25 Hamered Street, 68125 Tel Aviv, Israel.
authors.forename: Stefano
authors.initials: S
authors.lastname: Boccaletti