The DOI matches its Crossref record; 19 of the 19 references it cites were found in a registry or an index.
The Kuramoto model in complex networks
Open accessAbstract
Synchronization of an ensemble of oscillators is an emergent phenomenon present in several complex systems, ranging from social and physical to biological and technological systems. The most successful approach to describe how coherent behavior emerges in these complex systems is given by the paradigmatic Kuramoto model. This model has been traditionally studied in complete graphs. However, besides being intrinsically dynamical, complex systems present very heterogeneous structure, which can be represented as complex networks. This report is dedicated to review main contributions in the field of synchronization in networks of Kuramoto oscillators. In particular, we provide an overview of the impact of network patterns on the local and global dynamics of coupled phase oscillators. We cover many relevant topics, which encompass a description of the most used analytical approaches and the analysis of several numerical results. Furthermore, we discuss recent developments on variations of the Kuramoto model in networks, including the presence of noise and inertia. The rich potential for applications is discussed for special fields in engineering, neuroscience, physics and Earth science. Finally, we conclude by discussing problems that remain open after the last decade of intensive research on the Kuramoto model and point out some promising directions for future research.
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Cites
Emergence of Scaling in Random Networks
Barabási, A.-L., & Albert, R. (1999) · Science · doi:10.1126/science.286.5439.509 · Cited by 36,135
Finding and evaluating community structure in networks
Newman, M. E. J., & Girvan, M. (2004) · Physical Review E · doi:10.1103/physreve.69.026113 · Cited by 13,931
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
Newman, M. (2010) · doi:10.1093/acprof:oso/9780199206650.001.0001 · Cited by 6,595
Uncovering the overlapping community structure of complex networks in nature and society
Palla, G., Derényi, I., Farkas, I., & Vicsek, T. (2005) · Nature · doi:10.1038/nature03607 · Cited by 5,373
Hierarchical Organization of Modularity in Metabolic Networks
Ravasz, E., Somera, A. L., Mongru, D. A., Oltvai, Z. N., & Barabási, A.-L. (2002) · Science · doi:10.1126/science.1073374 · Cited by 4,224
The Geometry of Biological Time
Winfree, A. T. (1980) · doi:10.1007/978-3-662-22492-2 · Cited by 3,613
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
Dynamical Processes on Complex Networks
Barrat, A., Barthélemy, M., & Vespignani, A. (2008) · doi:10.1017/cbo9780511791383 · Cited by 2,704 · cited 9×
“All these efforts to uncover and characterize the modular structure of networks naturally raised questions about the role played by the presence of communities in dynamical processes [47].”
BackgroundMethodInfluentialDorogovtsev, S. N., & Mendes, J. F. F. (2003) · doi:10.1093/acprof:oso/9780198515906.001.0001 · Cited by 1,563
Communicability in complex networks
Estrada, E., & Hatano, N. (2008) · Physical Review E · doi:10.1103/physreve.77.036111 · Cited by 719
Broadband criticality of human brain network synchronization
Kitzbichler, M. G., Smith, M. L., Christensen, S. R., & Bullmore, E. (2009) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1000314 · Cited by 527
Barabási, A.-L. (2012) · Nature Physics · doi:10.1038/nphys2188 · Cited by 502
Avalanche Collapse of Interdependent Networks
Baxter, G. J., Dorogovtsev, S. N., Goltsev, A. V., & Mendes, J. F. F. (2012) · Physical Review Letters · doi:10.1103/physrevlett.109.248701 · Cited by 376
Mathematical framework for large-scale brain network modeling in The Virtual Brain
Sanz-Leon, P., Knock, S. A., Spiegler, A., & Jirsa, V. K. (2015) · NeuroImage · doi:10.1016/j.neuroimage.2015.01.002 · Cited by 356 · cited 1×
“Other recent works have investigated further aspects of the relation between structure and dynamics of phase oscillators in anatomical and functional cortical networks [214, 378, 401–406], which includes studies on the effects of remote synchronization [407–409], a toolbox for large-scale simulations of brain dynamics…”
BackgroundDynamical consequences of lesions in cortical networks
Honey, C. J., & Sporns, O. (2008) · Human Brain Mapping · doi:10.1002/hbm.20579 · Cited by 353
Exploring the network dynamics underlying brain activity during rest
Cabral, J., Kringelbach, M. L., & Deco, G. (2014) · Progress in Neurobiology · doi:10.1016/j.pneurobio.2013.12.005 · Cited by 351
Interdisciplinary and physics challenges of network theory
Bianconi, G. (2015) · EPL (Europhysics Letters) · doi:10.1209/0295-5075/111/56001 · Cited by 126
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What are higher-order networks?
Bick, C., Gross, E., Harrington, H. A., & Schaub, M. T. (2023) · SIAM Review · doi:10.1137/21m1414024 · Cited by 420
Explosive transitions in complex networks’ structure and dynamics: Percolation and synchronization
Boccaletti, S., Almendral, J. A., Guan, S., Leyva, I., Liu, Z., Sendiña-Nadal, I., Wang, Z., & Zou, Y. (2016) · Physics Reports · doi:10.1016/j.physrep.2016.10.004 · Cited by 363
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
Dissecting whole-brain conduction delays through MRI microstructural measures
Mancini, M., Tian, Q., Fan, Q., Cercignani, M., & Huang, S. Y. (2021) · Brain Structure and Function · doi:10.1007/s00429-021-02358-w · Cited by 20
Metadata
- Authors
- Rodrigues, F. A., Peron, T. K. D., Ji, P., & Kurths, J.
- Venue
- Physics Reports
- Publisher
- Elsevier BV
- Published
- 2016-01
- Volume
- 610
- Pages
- 1-98
- ISSN
- 0370-1573 (ISSN-L)
- OpenAlex
- W2153706317
- Cited by
- 1,040
- References
- 19
- FWCI
- 77.13
- Type
- journal article
- Language
- en
- Open access
- hybrid
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