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Low dimensional behavior of large systems of globally coupled oscillators
Open accessAbstract
It is shown that, in the infinite size limit, certain systems of globally coupled phase oscillators display low dimensional dynamics. In particular, we derive an explicit finite set of nonlinear ordinary differential equations for the macroscopic evolution of the systems considered. For example, an exact, closed form solution for the nonlinear time evolution of the Kuramoto problem with a Lorentzian oscillator frequency distribution function is obtained. Low dimensional behavior is also demonstrated for several prototypical extensions of the Kuramoto model, and time-delayed coupling is also considered.
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Cited by
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
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
Exact results for the Kuramoto model with a bimodal frequency distribution
Martens, E. A., Barreto, E., Strogatz, S. H., Ott, E., So, P., & Antonsen, T. M. (2009) · Physical Review E · doi:10.1103/physreve.79.026204 · Cited by 329
Self-citationResynchronization of circadian oscillators and the east-west asymmetry of jet-lag
Lu, Z., Klein-Cardeña, K., Lee, S., Antonsen, T. M., Girvan, M., & Ott, E. (2016) · Chaos: An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.4954275 · Cited by 75
Self-citationEffective theory of collective deep learning
Arola-Fernández, L., & Lacasa, L. (2024) · Physical Review Research · doi:10.1103/physrevresearch.6.l042040 · Cited by 3
Metadata
- Authors
- Ott, E., & Antonsen, T. M.
- Venue
- Chaos: An Interdisciplinary Journal of Nonlinear Science
- Publisher
- AIP Publishing
- Published
- 2008-09-01
- Volume
- 18
- Issue
- 3
- Pages
- 037113-037113
- ISSN
- 1054-1500 (ISSN-L)
- 1089-7682
- OpenAlex
- W2022904439
- Cited by
- 968
- References
- 0
- FWCI
- 39.51
- Type
- journal article
- Language
- en
- Open access
- green
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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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