The DOI matches its Crossref record.
Synchronization in Small-World Systems
Open accessAbstract
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.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cited by
The Structure and Function of Complex Networks
Newman, M. E. J. (2003) · SIAM Review · doi:10.1137/s003614450342480 · Cited by 18,719
Complex brain networks: graph theoretical analysis of structural and functional systems
Bullmore, E., & Sporns, O. (2009) · Nature Reviews Neuroscience · doi:10.1038/nrn2575 · Cited by 11,820
Fortunato, S. (2010) · Physics Reports · doi:10.1016/j.physrep.2009.11.002 · Cited by 11,293
Complex networks: structure and dynamics
BOCCALETTI, S., LATORA, V, MORENO, Y., CHAVEZ, M., & HWANG, D. (2006) · Physics Reports · doi:10.1016/j.physrep.2005.10.009 · Cited by 11,010
Synchronization in complex networks
Arenas, A., Díaz-Guilera, A., Kurths, J., Moreno, Y., & Zhou, C. (2008) · Physics Reports · doi:10.1016/j.physrep.2008.09.002 · Cited by 3,713
The structure and dynamics of multilayer networks
Boccaletti, S., Bianconi, G., Criado, R., del Genio, C. I., Gómez-Gardeñes, J., Romance, M., Sendiña-Nadal, I., Wang, Z., & Zanin, M. (2014) · Physics Reports · doi:10.1016/j.physrep.2014.07.001 · Cited by 3,125
Bassett, D. S., & Bullmore, E. (2006) · The Neuroscientist · doi:10.1177/1073858406293182 · Cited by 2,600
Barthélemy, M. (2011) · Physics Reports · doi:10.1016/j.physrep.2010.11.002 · Cited by 2,469
Critical phenomena in complex networks
Dorogovtsev, S. N., Goltsev, A. V., & Mendes, J. F. F. (2008) · Reviews of Modern Physics · doi:10.1103/revmodphys.80.1275 · Cited by 2,220
Network ‘Small-World-Ness’: A Quantitative Method for Determining Canonical Network Equivalence
Humphries, M. D., & Gurney, K. (2008) · PLoS ONE · doi:10.1371/journal.pone.0002051 · Cited by 1,442
Diffusion Dynamics on Multiplex Networks
Gómez, S., Díaz-Guilera, A., Gómez-Gardeñes, J., Pérez-Vicente, C. J., Moreno, Y., & Arenas, A. (2013) · Physical Review Letters · doi:10.1103/physrevlett.110.028701 · Cited by 1,003
Structural Properties of the Caenorhabditis elegans Neuronal Network
Varshney, L. R., Chen, B. L., Paniagua, E., Hall, D. H., & Chklovskii, D. B. (2011) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1001066 · Cited by 867
Adaptive reconfiguration of fractal small-world human brain functional networks
Bassett, D. S., Meyer-Lindenberg, A., Achard, S., Duke, T., & Bullmore, E. (2006) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0606005103 · Cited by 814
Entropy measures for networks: Toward an information theory of complex topologies
Anand, K., & Bianconi, G. (2009) · Physical Review E · doi:10.1103/physreve.80.045102 · Cited by 368
Bartolomei, F., Bosma, I., Klein, M., Baayen, J. C., Reijneveld, J. C., Postma, T. J., Heimans, J. J., van Dijk, B. W., de Munck, J. C., de Jongh, A., et al. (2006) · Clinical Neurophysiology · doi:10.1016/j.clinph.2006.05.018 · Cited by 276
Dyhrfjeld-Johnsen, J., Santhakumar, V., Morgan, R. J., Huerta, R., Tsimring, L., & Soltesz, I. (2007) · Journal of Neurophysiology · doi:10.1152/jn.00950.2006 · Cited by 230
Topological Strata of Weighted Complex Networks
Petri, G., Scolamiero, M., Donato, I., & Vaccarino, F. (2013) · PLoS ONE · doi:10.1371/journal.pone.0066506 · Cited by 214
The brain matures with stronger functional connectivity and decreased randomness of its network
Smit, D. J. A., Boersma, M., Schnack, H. G., Micheloyannis, S., Boomsma, D. I., Hulshoff Pol, H. E., Stam, C. J., & de Geus, E. J. C. (2012) · PLoS ONE · doi:10.1371/journal.pone.0036896 · Cited by 143
Coevolutionary networks with homophily and heterophily
Kimura, D., & Hayakawa, Y. (2008) · Physical Review E · doi:10.1103/physreve.78.016103 · Cited by 107
Dynamic synchronization of extreme heat in complex climate networks in the contiguous United States
Wang, Z.-H., Wang, C., & Yang, X. (2021) · Urban Climate · doi:10.1016/j.uclim.2021.100909 · Cited by 20
Metadata
- Authors
- Barahona, M., & Pecora, L. M.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2002-07-16
- Volume
- 89
- Issue
- 5
- Pages
- 054101-054101
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2014217492
- Cited by
- 1,638
- References
- 0
- FWCI
- 37.93
- Type
- journal article
- Language
- en
- Open access
- green
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
