Hyperbolic chaos at blinking coupling of noisy oscillators
- We study an ensemble of identical noisy phase oscillators with a blinking mean-field coupling, where onecluster and two-cluster synchronous states alternate. In the thermodynamic limit the population is described by a nonlinear Fokker-Planck equation. We show that the dynamics of the order parameters demonstrates hyperbolic chaos. The chaoticity manifests itself in phases of the complex mean field, which obey a strongly chaotic Bernoulli map. Hyperbolicity is confirmed by numerical tests based on the calculations of relevant invariant Lyapunov vectors and Lyapunov exponents. We show how the chaotic dynamics of the phases is slightly smeared by finite-size fluctuations. DOI: 10.1103/PhysRevE.87.032912
| Author details: | Pavel V. Kuptsov, Sergey P. Kuznetsov, Arkadij PikovskijORCiDGND |
|---|---|
| DOI: | https://doi.org/10.1103/PhysRevE.87.032912 |
| ISSN: | 1539-3755 |
| Title of parent work (English): | Physical review : E, Statistical, nonlinear and soft matter physics |
| Publisher: | American Physical Society |
| Place of publishing: | College Park |
| Publication type: | Article |
| Language: | English |
| Year of first publication: | 2013 |
| Publication year: | 2013 |
| Release date: | 2017/03/26 |
| Volume: | 87 |
| Issue: | 3 |
| Number of pages: | 7 |
| Funding institution: | RFBR [11-02-91334]; DFG [PI 220/14-1] |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
| Peer review: | Referiert |
