Twisted States in a System of Nonlinearly Coupled Phase Oscillators
- We study the dynamics of the ring of identical phase oscillators with nonlinear nonlocal coupling. Using the Ott - Antonsen approach, the problem is formulated as a system of partial derivative equations for the local complex order parameter. In this framework, we investigate the existence and stability of twisted states. Both fully coherent and partially coherent stable twisted states were found (the latter ones for the first time for identical oscillators). We show that twisted states can be stable starting from a certain critical value of the medium length, or on a length segment. The analytical results are confirmed with direct numerical simulations in finite ensembles.
| Author details: | Dmitry BolotovORCiD, Maxim I. BolotovORCiD, Lev A. SmirnovORCiD, Grigory V. OsipovORCiDGND, Arkadij PikovskijORCiDGND |
|---|---|
| DOI: | https://doi.org/10.1134/S1560354719060091 |
| ISSN: | 1560-3547 |
| ISSN: | 1468-4845 |
| Title of parent work (English): | Regular and chaotic dynamics : international scientific journal |
| Publisher: | Pleiades publishing inc |
| Place of publishing: | Moscow |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2019/12/10 |
| Publication year: | 2019 |
| Release date: | 2020/10/06 |
| Tag: | Ott - Antonsen reduction; nonlocal coupling; phase oscillators; stability analysis; twisted state |
| Volume: | 24 |
| Issue: | 6 |
| Number of pages: | 8 |
| First page: | 717 |
| Last Page: | 724 |
| Funding institution: | RFBRRussian Foundation for Basic Research (RFBR) [19-52-12053]; RSFRussian Science Foundation (RSF) [19-1200367] |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik |
| Peer review: | Referiert |
