title: Tweaking synchronization by connectivity modifications.
abstract: Natural and man-made networks often possess locally treelike substructures. Taking such tree networks as our starting point, we show how the addition of links changes the synchronization properties of the network. We focus on two different methods of link addition. The first method adds single links that create cycles of a well-defined length. Following a topological approach, we introduce cycles of varying length and analyze how this feature, as well as the position in the network, alters the synchronous behavior. We show that in particular short cycles can lead to a maximum change of the Laplacian's eigenvalue spectrum, dictating the synchronization properties of such networks. The second method connects a certain proportion of the initially unconnected nodes. We simulate dynamical systems on these network topologies, with the nodes' local dynamics being either discrete or continuous. Here our main result is that a certain number of additional links, with the relative position in the network being crucial, can be beneficial to ensure stable synchronization.
authors.affiliation: Potsdam Institute for Climate Impact Research, P.O. Box 60 12 03, 14412 Potsdam, Germany.|Department of Physics, Humboldt University of Berlin, Newtonstrasse 15, 12489 Berlin, Germany.
authors.forename: Paul
authors.initials: P
authors.lastname: Schultz
authors.affiliation: Potsdam Institute for Climate Impact Research, P.O. Box 60 12 03, 14412 Potsdam, Germany.|Instituto de Física de São Carlos, Universidade de São Paulo, São Carlos, São Paulo, Brazil.
authors.forename: Thomas
authors.initials: T
authors.lastname: Peron
authors.affiliation: Potsdam Institute for Climate Impact Research, P.O. Box 60 12 03, 14412 Potsdam, Germany.|Department of Physics, Humboldt University of Berlin, Newtonstrasse 15, 12489 Berlin, Germany.
authors.forename: Deniz
authors.initials: D
authors.lastname: Eroglu
authors.affiliation: School of Mathematics and Statistics, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia.
authors.forename: Thomas
authors.initials: T
authors.lastname: Stemler
authors.affiliation: Instituto de Investigaciones Físicas, Casilla 8635, Universidad Mayor de San Andrés, La Paz, Bolivia.
authors.forename: Gonzalo Marcelo
authors.initials: GM
authors.lastname: Ramírez Ávila
authors.affiliation: Instituto de Ciências Matemáticas e de Computaçao, Universidade de São Paulo, CP 668, 13560-970 São Carlos, São Paulo, Brazil.
authors.forename: Francisco A
authors.initials: FA
authors.lastname: Rodrigues
authors.affiliation: Potsdam Institute for Climate Impact Research, P.O. Box 60 12 03, 14412 Potsdam, Germany.|Department of Physics, Humboldt University of Berlin, Newtonstrasse 15, 12489 Berlin, Germany.|Institute for Complex Systems and Mathematical Biology, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom.|Department of Control Theory, Nizhny Novgorod State University, Gagarin Avenue 23, 606950 Nizhny Novgorod, Russia.
authors.forename: Jürgen
authors.initials: J
authors.lastname: Kurths