title: Generalized synchronization in relay systems with instantaneous coupling.
abstract: We demonstrate the existence of generalized synchronization in systems that act as mediators between two dynamical units that, in turn, show complete synchronization with each other. These are the so-called relay systems. Specifically, we analyze the Lyapunov spectrum of the full system to elucidate when complete and generalized synchronization appear. We show that once a critical coupling strength is achieved, complete synchronization emerges between the systems to be synchronized, and at the same point, generalized synchronization with the relay system also arises. Next, we use two nonlinear measures based on the distance between phase-space neighbors to quantify the generalized synchronization in discretized time series. Finally, we experimentally show the robustness of the phenomenon and of the theoretical tools here proposed to characterize it.
authors: Department of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100, Israel.
authors: R
authors: R
authors: Gutiérrez
authors: Centro Universitario de los Lagos, Universidad de Guadalajara, Lagos de Moreno, Jalisco 47460, Mexico and Complex Systems Group, Universidad Rey Juan Carlos, 28933 Móstoles, Madrid, Spain.
authors: R
authors: R
authors: Sevilla-Escoboza
authors: Institute for Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza, Zaragoza 50009, Spain.
authors: P
authors: P
authors: Piedrahita
authors: d-fine GmbH, Opernplatz 2, 60313 Frankfurt, Germany.
authors: C
authors: C
authors: Finke
authors: ICBM, University of Oldenburg, Carl-von-Ossietzky-Strasse 9-11, 26111 Oldenburg, Germany and IPST, University of Maryland, College Park, Maryland 20742-2431, USA.
authors: U
authors: U
authors: Feudel
authors: Complex Systems Group, Universidad Rey Juan Carlos, 28933 Móstoles, Madrid, Spain and Center for Biomedical Technology, Technical University of Madrid, Pozuelo de Alarcón, 28223 Madrid, Spain.
authors: J M
authors: JM
authors: Buldú
authors: Centro Universitario de los Lagos, Universidad de Guadalajara, Lagos de Moreno, Jalisco 47460, Mexico.
authors: G
authors: G
authors: Huerta-Cuellar
authors: Centro Universitario de los Lagos, Universidad de Guadalajara, Lagos de Moreno, Jalisco 47460, Mexico.
authors: R
authors: R
authors: Jaimes-Reátegui
authors: Institute for Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza, Zaragoza 50009, Spain and Department of Theoretical Physics, University of Zaragoza, Zaragoza 50009, Spain and Complex Networks and Systems Lagrange Lab, Institute for Scientific Interchange, Turin, Italy.
authors: Y
authors: Y
authors: Moreno
authors: CNR Institute of Complex Systems, Via Madonna del Piano, 10, 50019 Sesto Fiorentino, Florence, Italy.
authors: S
authors: S
authors: Boccaletti