title: Observability coefficients for predicting the class of synchronizability from the algebraic structure of the local oscillators.
abstract: Understanding the conditions under which a collective dynamics emerges in a complex network is still an open problem. A useful approach is the master stability function-and its related classes of synchronization-which offers a necessary condition to assess when a network successfully synchronizes. Observability coefficients, on the other hand, quantify how well the original state space of a system can be observed given only the access to a measured variable. The question is therefore pertinent: Given a generic dynamical system (represented by a state variable x) and given a generic measure on it h(x) (which may be either an observation of an external agent, or an output function through which the units of a network interact), are classes of synchronization and observability actually related to each other? We explicitly address this issue, and show a series of nontrivial relationships for networks of different popular chaotic systems (Rössler, Lorenz, and Hindmarsh-Rose oscillators). Our results suggest that specific dynamical properties can be evoked for explaining the classes of synchronizability.
authors.affiliation: Complex Systems Group, Universidad Rey Juan Carlos, E-28933 Móstoles, Madrid, Spain.|Center for Biomedical Technology, Universidad Politécnica de Madrid, E-28223 Pozuelo de Alarcón, Madrid, Spain.
authors.forename: Irene
authors.initials: I
authors.lastname: Sendiña-Nadal
authors.affiliation: CNR-Institute of Complex Systems, Via Madonna del Piano, 10, I-50019 Sesto Fiorentino, Florence, Italy.|Italian Embassy in Israel, 25 Hamered Street, 68125 Tel Aviv, Israel.
authors.forename: Stefano
authors.initials: S
authors.lastname: Boccaletti
authors.affiliation: CORIA UMR 6614-Normandie Université, CNRS et INSA de Rouen, Campus Universitaire du Madrillet, F-76800 Saint-Etienne du Rouvray, France.
authors.forename: Christophe
authors.initials: C
authors.lastname: Letellier