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Spectral properties of chimera states
Abstract
Chimera states are particular trajectories in systems of phase oscillators with nonlocal coupling that display a spatiotemporal pattern of coherent and incoherent motion. We present here a detailed analysis of the spectral properties for such trajectories. First, we study numerically their Lyapunov spectrum and its behavior for an increasing number of oscillators. The spectra demonstrate the hyperchaotic nature of the chimera states and show a correspondence of the Lyapunov dimension with the number of incoherent oscillators. Then, we pass to the thermodynamic limit equation and present an analytic approach to the spectrum of a corresponding linearized evolution operator. We show that, in this setting, the chimera state is neutrally stable and that the continuous spectrum coincides with the limit of the hyperchaotic Lyapunov spectrum obtained for the finite size systems.
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Compte, A. (2000) · Cerebral Cortex · doi:10.1093/cercor/10.9.910 · Cited by 1,143
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
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
- Wolfrum, M., Omel’chenko, O. E., Yanchuk, S., & Maistrenko, Y. L.
- Venue
- Chaos: An Interdisciplinary Journal of Nonlinear Science
- Publisher
- AIP Publishing
- Published
- 2011-03-01
- Volume
- 21
- Issue
- 1
- Pages
- 013112-013112
- ISSN
- 1054-1500 (ISSN-L)
- 1089-7682
- OpenAlex
- W2054345627
- Cited by
- 185
- References
- 1
- FWCI
- 10.97
- Type
- journal article
- Language
- en
- Open access
- closed
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- Wolfrum, M., Omel’chenko, O. E., Yanchuk, S., & Maistrenko, Y. L. (2011). Spectral properties of chimera states. Chaos: An Interdisciplinary Journal of Nonlinear Science. https://doi.org/10.1063/1.3563579
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