title: Network-complement transitions, symmetries, and cluster synchronization.
abstract: Synchronization in networks of coupled oscillators is known to be largely determined by the spectral and symmetry properties of the interaction network. Here, we leverage this relation to study a class of networks for which the threshold coupling strength for global synchronization is the lowest among all networks with the same number of nodes and links. These networks, defined as being uniform, complete, and multi-partite (UCM), appear at each of an infinite sequence of network-complement transitions in a larger class of networks characterized by having near-optimal thresholds for global synchronization. We show that the distinct symmetry structure of the UCM networks, which by design are optimized for global synchronizability, often leads to formation of clusters of synchronous oscillators, and that such states can coexist with the state of global synchronization.
authors: Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, USA.
authors: Takashi
authors: T
authors: Nishikawa
authors: Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, USA.
authors: Adilson E
authors: AE
authors: Motter