Heterogeneity in oscillator networks: are smaller worlds easier to synchronize?

By Takashi Nishikawa, Adilson E. Motter, Ying-Cheng Lai, Frank C. Hoppensteadt. Physical Review Letters, 2003

758 citations recorded by the source corpus.

Small-world and scale-free networks are known to be more easily synchronized than regular lattices, which is usually attributed to the smaller network distance between oscillators. Surprisingly, we find that networks with a homogeneous distribution of connectivity are more synchronizable than heterogeneous ones, even though the average network distance is larger. We present numerical computations and analytical estimates on synchronizability of the network in terms of its heterogeneity parameters. Our results suggest that some degree of homogeneity is expected in naturally evolved structures, such as neural networks, where synchronizability is desirable.

Subfields: Computer Networks and Communications, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/97c4a2ca92fd0e950e5026e769f1abe4f2fc3fa3

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In Computer Networks and Communications

In Statistical and Nonlinear Physics

Citations in the corpus

The application of graph theoretical analysis to complex networks in the brain. (2007, neutral): “In particular, the eigenvalue ratio R = kN/k2, which is the ratio of the largest and second smallest eigenvalue of a graph, may be a useful indicator of synchronizability (Nishikawa et al., 2003; Boccaletti et al., 2006).”
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].”
Dynamics and Effective Topology Underlying Synchronization in Networks of Cortical Neurons (2006, positive): “As explained above, under certain conditions that might be applicable to neuronal networks (Nishikawa et al., 2003; Motter et al., 2005), dynamic systems coupled in this way display enhanced signal propagation speed that is invariant or even decreases with network size (Strogatz, 2001; Newman, 2003;”
Explosive transitions in complex networks’ structure and dynamics: Percolation and synchronization (2016, background): “Reference [257] further elaborated on the role of heterogeneity, and realized that heterogeneous structures may display very large ratios λN/λ2 (λN scales with the hub’s degree, i.”
Small-World Brain Networks Revisited (2016, background): “Perhaps the most commonly studied function aﬀorded by small-world architecture is the ability to transmit information, a characteristic that is common in networks of coupled oscillators [115–117] (although see [118] for a few notable exceptions).”
Control Principles of Complex Networks (2015, background): “At the same time we learned that the topology fundamentally affects the dynamical processes taking place on these networks, from epidemic spreading (Cohen et al., 2000; Pastor-Satorras and Vespignani, 2001) to synchronization (Nishikawa et al., 2003; Wang and Slotine, 2005).”