Paths to synchronization on complex networks.

By Jesús Gómez-Gardeñes, Yamir Moreno, Alex Arenas. Physical Review Letters, 2006

343 citations recorded by the source corpus.

The understanding of emergent collective phenomena in natural and social systems has driven the interest of scientists from different disciplines during decades. Among these phenomena, the synchronization of a set of interacting individuals or units has been intensively studied because of its ubiquity in the natural world. In this Letter, we show how for fixed coupling strengths local patterns of synchronization emerge differently in homogeneous and heterogeneous complex networks, driving the process towards a certain global synchronization degree following different paths. The dependence of the dynamics on the coupling strength and on the topology is unveiled. This study provides a new perspective and tools to understand this emerging phenomena.

Subfields: Computer Networks and Communications, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/51071c2d1c34d7fd4d721d2fcaaf78aeb3e8165f

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In Computer Networks and Communications

In Statistical and Nonlinear Physics

Citations in the corpus

The Kuramoto model in complex networks (2015, background): “However, a measure of synchronization given by a combination of the global order parameter and the measure of pairwise coherence of links as a local measure of synchronization was assumed [273],”
Synchronization in complex networks (2008, methodology): “In fact, several further investigations have shown that the highly connected oscillators synchronize faster among them and form synchronization clusters [48, 116, 117, 39], which is in contrast with the argument provided in [103].”
Structure and Dynamics of Networks (2009, background): “Recent studies [Gomez-Gardenes et al., 2007a] on Barabási-Albert networks, which have a scale-free degree distribution, γ = 3, and particular further properties due to their construction scheme, revealed a dominance of the cooperation strategy, a behavior previously unobserved.”
Explosive transitions in complex networks’ structure and dynamics: Percolation and synchronization (2016, background): “[302] compared the synchronization patterns in ER and SF networks and showed that even in the incoherent solution, the system self-organizes following different paths: while in SF networks the giant component of the synchronized pairs is gradually increasing with the coupling strength around the lar”
Critical phenomena in complex networks (2007, methodology): “The evolution of synchronization in the Kuramoto model on the Erdős-Rényi and scale-free networks was recently studied by Gómez-Gardeñes et al. (2007). These authors solved numerically Eq. (124) for N = 1000 coupled phase oscillators and demonstrated that (i) the synchronization on a scale-free netw”
Synchronization in complex networks of phase oscillators: A survey (2014, background): “, 2013), the weighted nodal degree degi = ∑n j=1 aij (Wu and Kumagai, 1982; Korniss et al., 2006; Gómez-Gardeñes et al., 2007; Buzna et al., 2009; Dörfler and Bullo, 2012b, 2013a; Skardal et al., 2013), or various metrics related to the notion of effective resistance (Wu and Kumagai, 1982; Korniss e”