Two-Bunch Solutions for the Dynamics of Ott–Antonsen Phase Ensembles
- We have developed a method for deriving systems of closed equations for the dynamics of order parameters in the ensembles of phase oscillators. The Ott-Antonsen equation for the complex order parameter is a particular case of such equations. The simplest nontrivial extension of the Ott-Antonsen equation corresponds to two-bunch states of the ensemble. Based on the equations obtained, we study the dynamics of multi-bunch chimera states in coupled Kuramoto-Sakaguchi ensembles. We show an increase in the dimensionality of the system dynamics for two-bunch chimeras in the case of identical phase elements and a transition to one-bunch "Abrams chimeras" for imperfect identity (in the latter case, the one-bunch chimeras become attractive).
| Author details: | Irina V. Tyulkina, Denis S. GoldobinGND, Lyudmila S. KlimenkoORCiD, Arkadij PikovskijORCiDGND |
|---|---|
| DOI: | https://doi.org/10.1007/s11141-019-09924-7 |
| ISSN: | 0033-8443 |
| ISSN: | 1573-9120 |
| Title of parent work (English): | Radiophysics and Quantum Electronics |
| Publisher: | Springer |
| Place of publishing: | New York |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2019/03/21 |
| Publication year: | 2019 |
| Release date: | 2021/05/17 |
| Volume: | 61 |
| Issue: | 8-9 |
| Number of pages: | 10 |
| First page: | 640 |
| Last Page: | 649 |
| Funding institution: | Russian Science Foundation Russian Science Foundation (RSF) [14-12-00811]; Russian Federation Russian Federation [MK-1447.2017.5, G-RICS M-2017b-5] |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik |
| Peer review: | Referiert |
