Chimera patterns in the Kuramoto-Battogtokh model
- Kuramoto and Battogtokh (2002 Nonlinear Phenom. Complex Syst. 5 380) discovered chimera states represented by stable coexisting synchrony and asynchrony domains in a lattice of coupled oscillators. After a reformulation in terms of a local order parameter, the problem can be reduced to partial differential equations. We find uniformly rotating, spatially periodic chimera patterns as solutions of a reversible ordinary differential equation, and demonstrate a plethora of such states. In the limit of neutral coupling they reduce to analytical solutions in the form of one-and two-point chimera patterns as well as localized chimera solitons. Patterns at weakly attracting coupling are characterized by virtue of a perturbative approach. Stability analysis reveals that only the simplest chimeras with one synchronous region are stable.
Author details: | Lev A. SmirnovORCiD, Grigory V. OsipovORCiDGND, Arkadij PikovskijORCiDGND |
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DOI: | https://doi.org/10.1088/1751-8121/aa55f1 |
ISSN: | 1751-8113 |
ISSN: | 1751-8121 |
Title of parent work (English): | Journal of physics : A, Mathematical and theoretical |
Publisher: | IOP Publ. Ltd. |
Place of publishing: | Bristol |
Publication type: | Article |
Language: | English |
Date of first publication: | 2017/01/16 |
Publication year: | 2017 |
Release date: | 2022/06/24 |
Tag: | Ott-Antonsen reduction; chimera state; coarse-grained order parameter; linear stability analysis; nonlocal coupled oscillators; perturbation approach |
Volume: | 50 |
Issue: | 8 |
Number of pages: | 10 |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
DDC classification: | 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik |
Peer review: | Referiert |