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From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators
Open accessAbstract
The Kuramoto model describes a large population of coupled limit-cycle oscillators whose natural frequencies are drawn from some prescribed distribution. If the coupling strength exceeds a certain threshold, the system exhibits a phase transition: some of the oscillators spontaneously synchronize, while others remain incoherent. The mathematical analysis of this bifurcation has proved both problematic and fascinating. We review 25 years of research on the Kuramoto model, highlighting the false turns as well as the successes, but mainly following the trail leading from Kuramoto’s work to Crawford’s recent contributions. It is a lovely winding road, with excursions through mathematical biology, statistical physics, kinetic theory, bifurcation theory, and plasma physics.
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Cites
The Geometry of Biological Time
Winfree, A. T. (1980) · doi:10.1007/978-3-662-22492-2 · Cited by 3,613
Cited by
Consensus and Cooperation in Networked Multi-Agent Systems
Olfati-Saber, R., Fax, J. A., & Murray, R. M. (2007) · Proceedings of the IEEE · doi:10.1109/jproc.2006.887293 · Cited by 10,522
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
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
Sumpter, D. J. T. (2010) · doi:10.1515/9781400837106 · Cited by 914
Chimera states: coexistence of coherence and incoherence in networks of coupled oscillators
Panaggio, M. J., & Abrams, D. M. (2015) · Nonlinearity · doi:10.1088/0951-7715/28/3/r67 · Cited by 788
Metadata
- Authors
- Strogatz, S. H.
- Venue
- Physica D: Nonlinear Phenomena
- Publisher
- Elsevier BV
- Published
- 2000-09
- Volume
- 143
- Issue
- 1-4
- Pages
- 1-20
- ISSN
- 0167-2789 (ISSN-L)
- OpenAlex
- W2130518506
- Cited by
- 3,051
- References
- 1
- FWCI
- 27.88
- Type
- journal article
- Language
- en
- Open access
- hybrid
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- Strogatz, S. H. (2000). From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators. Physica D: Nonlinear Phenomena. https://doi.org/10.1016/s0167-2789(00)00094-4
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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