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The mathematics behind chimera states
Abstract
Abstract Chimera states are self-organized spatiotemporal patterns of coexisting coherence and incoherence. We give an overview of the main mathematical methods used in studies of chimera states, focusing on chimera states in spatially extended coupled oscillator systems. We discuss the continuum limit approach to these states, Ott-Antonsen manifold reduction, finite size chimera states, control of chimera states and the influence of system design on the type of chimera state that is observed.
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Cited by
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
Parastesh, F., Jafari, S., Azarnoush, H., Shahriari, Z., Wang, Z., Boccaletti, S., & Perc, M. (2021) · Physics Reports · doi:10.1016/j.physrep.2020.10.003 · Cited by 291
Metadata
- Authors
- Omel’chenko, O. E.
- Venue
- Nonlinearity
- Publisher
- IOP Publishing
- Published
- 2018-04-04
- Volume
- 31
- Issue
- 5
- Pages
- R121-R164
- ISSN
- 0951-7715 (ISSN-L)
- 1361-6544
- OpenAlex
- W2795749429
- Cited by
- 195
- References
- 0
- FWCI
- 14.47
- Type
- journal article
- Language
- en
- Open access
- closed
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- Omel’chenko, O. E. (2018). The mathematics behind chimera states. Nonlinearity. https://doi.org/10.1088/1361-6544/aaaa07
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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.
