Synchronization in small-world systems.

By Mauricio Barahona, L. Pecora. Physical Review Letters, 2001

1,466 citations recorded by the source corpus.

We quantify the dynamical implications of the small-world phenomenon by considering the generic synchronization of oscillator networks of arbitrary topology. The linear stability of the synchronous state is linked to an algebraic condition of the Laplacian matrix of the network. Through numerics and analysis, we show how the addition of random shortcuts translates into improved network synchronizability. Applied to networks of low redundancy, the small-world route produces synchronizability more efficiently than standard deterministic graphs, purely random graphs, and ideal constructive schemes. However, the small-world property does not guarantee synchronizability: the synchronization threshold lies within the boundaries, but linked to the end of the small-world region.

Subfields: Computer Networks and Communications, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/f067de520d6abc6e0ef1672e895b3497a3ae09a5

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Citations in the corpus

Characterizing the synchronizability of small-world dynamical networks (2004, background): “Although there are many papers which discuss the network synchronization problem [8]–[10], [15], [23]–[26], there are few results reported in the literature on how to rigorously characterize the network synchronizability.”
Sufficient Conditions for Fast Switching Synchronization in Time-Varying Network Topologies (2005, methodology): “For example, static networks are assumed for the analysis of [47, 48, 6].”
Synchronization in complex networks (2008, methodology): “Note that in the above investigations different structural properties change at the same time [91, 100, 103] when the parameters characterizing the original networks are modified.”
Decentralised minimal-time consensus (2011, background): “Various applications can be cast in this framework, including swarming and ﬂocking [1], [2], distributed computing [3], agreement in social networks [4], [5] or synchronisation of coupled oscillators [6], [7], [8].”
Synchronization and desynchronization of complex dynamical networks: an engineering viewpoint (2003, background): “In some other complex networks, for example, with only coupling through a few of the variables, i.e., with too large, the coupling strength may lead to desynchronization instead [ 6 ], [18], [24], [25], and [28].”
On partial contraction analysis for coupled nonlinear oscillators (2004, background): “They also conjectured that synchronizability is enhanced if the node is endowed with dynamics, which Barahona and Pecora showed numerically ( Barahona and Pecora 2002 ).”
GRETNA: a graph theoretical network analysis toolbox for imaging connectomics (2015, background): “, 2005), local efficiency and global efficiency (Latora and Marchiori, 2001, 2003), modularity (Newman, 2006), assortativity (Newman, 2002; Leung and Chau, 2007), synchronization (Barahona and Pecora, 2002; Motter et al., 2005) and hierarchy (Ravasz and Barabási, 2003).”
The small world of the cerebral cortex (2007, background): “erating complex dynamics (Sporns, 2004), an increased propensity for synchronization (Barahona and Pecora, 2002), efficient information exchange (Latora and Marchiori, 2001), and efficient navigability of information and social networks (Kleinberg, 2000).”
Small-world networks and functional connectivity in Alzheimer's disease. (2006, background): “It has been suggested that a small world--like network architecture may be optimal for synchronizing neural activity between different brain regions (Lago-Fernandez and others 2000; Latora and Marchiori 2001; Barahona and Pecora 2002; Masuda and Aihara 2004).”
Networks beyond pairwise interactions: structure and dynamics (2020, methodology): “The existence and stability of synchronization and cluster synchronization was assessed via Lyapunov exponents through the Master Stability Function (MSF) formalism [6, 359, 410].”
Critical phenomena in complex networks (2007, background): “First (mostly numerical) studies of various dynamical models have already revealed that the ability to synchronize can be improved in small-world networks (Barahona and Pecora, 2002; Gade and Hu, 2000; Hong et al., 2002a; Jost and Joy, 2001; Lago-Fernández et al., 2000; Wang and Chen, 2002).”
Network ‘Small-World-Ness’: A Quantitative Method for Determining Canonical Network Equivalence (2008, methodology): “Membership of the ‘small-world’ network class also implies that the corresponding systems have dynamic properties different from those of equivalent random or regular networks [3–7].”