Travelling chimera states in systems of phase oscillators with asymmetric nonlocal coupling
- We study travelling chimera states in a ring of nonlocally coupled heterogeneous (with Lorentzian distribution of natural frequencies) phase oscillators. These states are coherence-incoherence patterns moving in the lateral direction because of the broken reflection symmetry of the coupling topology. To explain the results of direct numerical simulations we consider the continuum limit of the system. In this case travelling chimera states correspond to smooth travelling wave solutions of some integro-differential equation, called the Ott–Antonsen equation, which describes the long time coarse-grained dynamics of the oscillators. Using the Lyapunov–Schmidt reduction technique we suggest a numerical approach for the continuation of these travelling waves. Moreover, we perform their linear stability analysis and show that travelling chimera states can lose their stability via fold and Hopf bifurcations. Some of the Hopf bifurcations turn out to be supercritical resulting in the observation of modulated travelling chimera states.
Author details: | Oleh Omel'chenkoORCiDGND |
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URN: | urn:nbn:de:kobv:517-opus4-518141 |
DOI: | https://doi.org/10.25932/publishup-51814 |
ISSN: | 1866-8372 |
Title of parent work (English): | Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe |
Publication series (Volume number): | Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe (1169) |
Publication type: | Postprint |
Language: | English |
Date of first publication: | 2021/10/20 |
Publication year: | 2019 |
Publishing institution: | Universität Potsdam |
Release date: | 2021/10/20 |
Tag: | Ott–Antonsen equation; chimera states; continuation; forced symmetry breaking; nonlocally coupled phase oscillators; stability; travelling waves |
Issue: | 2 |
Number of pages: | 35 |
First page: | 611 |
Last Page: | 642 |
Source: | Nonlinearity 33 (2020) 2, 611–642 DOI: 10.1088/1361-6544/ab5cd8 |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik | |
Peer review: | Referiert |
Publishing method: | Open Access / Green Open-Access |
License (German): | Creative Commons - Namensnennung, 3.0 Deutschland |