title: Synchronization in slowly switching networks of coupled oscillators.
abstract: Networks whose structure of connections evolves in time constitute a big challenge in the study of synchronization, in particular when the time scales for the evolution of the graph topology are comparable with (or even longer than) those pertinent to the units' dynamics. We here focus on networks with a slow-switching structure, and show that the necessary conditions for synchronization, i.e. the conditions for which synchronization is locally stable, are determined by the time average of the largest Lyapunov exponents of transverse modes of the switching topologies. Comparison between fast- and slow-switching networks allows elucidating that slow-switching processes prompt synchronization in the cases where the Master Stability Function is concave, whereas fast-switching schemes facilitate synchronization for convex curves. Moreover, the condition of slow-switching enables the introduction of a control strategy for inducing synchronization in networks with arbitrary structure and coupling strength, which is of evident relevance for broad applications in real world systems.
authors: Department of Physics, East China Normal University, Shanghai 200241, China.
authors: Jie
authors: J
authors: Zhou
authors: Department of Physics, East China Normal University, Shanghai 200241, China.
authors: Yong
authors: Y
authors: Zou
authors: Department of Physics, East China Normal University, Shanghai 200241, China.
authors: Shuguang
authors: S
authors: Guan
authors: Department of Physics, East China Normal University, Shanghai 200241, China.
authors: Zonghua
authors: Z
authors: Liu
authors: CNR-Institute of Complex Systems, Via Madonna del Piano, 10, 50019 Sesto Fiorentino, Florence, Italy.|The Embassy of Italy in Tel Aviv, 25 Hamered street, 68125 Tel Aviv, Israel.
authors: S
authors: S
authors: Boccaletti