title: Synchronization in networks with multiple interaction layers.
abstract: The structure of many real-world systems is best captured by networks consisting of several interaction layers. Understanding how a multilayered structure of connections affects the synchronization properties of dynamical systems evolving on top of it is a highly relevant endeavor in mathematics and physics and has potential applications in several socially relevant topics, such as power grid engineering and neural dynamics. We propose a general framework to assess the stability of the synchronized state in networks with multiple interaction layers, deriving a necessary condition that generalizes the master stability function approach. We validate our method by applying it to a network of Rössler oscillators with a double layer of interactions and show that highly rich phenomenology emerges from this. This includes cases where the stability of synchronization can be induced even if both layers would have individually induced unstable synchrony, an effect genuinely arising from the true multilayer structure of the interactions among the units in the network.
authors.affiliation: School of Life Sciences, University of Warwick, Coventry CV4 7AL, U.K.
authors.forename: Charo I
authors.initials: CI
authors.lastname: Del Genio
authors.affiliation: Departamento de Física de la Materia Condensada, University of Zaragoza, 50009 Zaragoza, Spain.; Institute for Biocomputation and Physics of Complex Systems, University of Zaragoza, 50018 Zaragoza, Spain.
authors.forename: Jesús
authors.initials: J
authors.lastname: Gómez-Gardeñes
authors.affiliation: Department of Physics, Bar-Ilan University, 52900 Ramat Gan, Israel.
authors.forename: Ivan
authors.initials: I
authors.lastname: Bonamassa
authors.affiliation: CNR-Istituto dei Sistemi Complessi, Via Madonna del Piano, 10, 50019 Sesto Fiorentino, Italy.; Embassy of Italy in Israel, 25 Hamered Street, 68125 Tel Aviv, Israel.
authors.forename: Stefano
authors.initials: S
authors.lastname: Boccaletti
keywords: Multi-layer networks; master stability function; stability; synchronization