Analytical approach to synchronous states of globally coupled noisy rotators
- We study populations of globally coupled noisy rotators (oscillators with inertia) allowing a nonequilibrium transition from a desynchronized state to a synchronous one (with the nonvanishing order parameter). The newly developed analytical approaches resulted in solutions describing the synchronous state with constant order parameter for weakly inertial rotators, including the case of zero inertia, when the model is reduced to the Kuramoto model of coupled noise oscillators. These approaches provide also analytical criteria distinguishing supercritical and subcritical transitions to the desynchronized state and indicate the universality of such transitions in rotator ensembles. All the obtained analytical results are confirmed by the numerical ones, both by direct simulations of the large ensembles and by solution of the associated Fokker-Planck equation. We also propose generalizations of the developed approaches for setups where different rotators parameters (natural frequencies, masses, noise intensities, strengths and phaseWe study populations of globally coupled noisy rotators (oscillators with inertia) allowing a nonequilibrium transition from a desynchronized state to a synchronous one (with the nonvanishing order parameter). The newly developed analytical approaches resulted in solutions describing the synchronous state with constant order parameter for weakly inertial rotators, including the case of zero inertia, when the model is reduced to the Kuramoto model of coupled noise oscillators. These approaches provide also analytical criteria distinguishing supercritical and subcritical transitions to the desynchronized state and indicate the universality of such transitions in rotator ensembles. All the obtained analytical results are confirmed by the numerical ones, both by direct simulations of the large ensembles and by solution of the associated Fokker-Planck equation. We also propose generalizations of the developed approaches for setups where different rotators parameters (natural frequencies, masses, noise intensities, strengths and phase shifts in coupling) are dispersed.…
Author details: | Vyacheslav MunyaevORCiD, Lev A. SmirnovORCiD, Vasily KostinORCiD, Grigory V. OsipovORCiDGND, Arkadij PikovskijORCiDGND |
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URN: | urn:nbn:de:kobv:517-opus4-524261 |
DOI: | https://doi.org/10.25932/publishup-52426 |
ISSN: | 1866-8372 |
Title of parent work (German): | Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe |
Publication series (Volume number): | Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe (1188) |
Publication type: | Postprint |
Language: | English |
Date of first publication: | 2019/11/15 |
Publication year: | 2020 |
Publishing institution: | Universität Potsdam |
Release date: | 2021/11/03 |
Tag: | Kuramoto model; coupled rotators; hysteresis; noisy systems; synchronization transition |
Issue: | 2 |
Article number: | 023036 |
Number of pages: | 17 |
Source: | New J. Phys. 22 023036 |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
DDC classification: | 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik |
Peer review: | Referiert |
Publishing method: | Open Access / Green Open-Access |
License (German): | CC-BY - Namensnennung 4.0 International |
External remark: | Bibliographieeintrag der Originalveröffentlichung/Quelle |