Isotropy of angular frequencies and weak chimeras with broken symmetry
The notion of a weak chimeras provides a tractable definition for chimera states in networks of finitely many phase oscillators. Here, we generalize the definition of a weak chimera to a more general class of equivariant dynamical systems by characterizing solutions in terms of the isotropy of their...
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| Format: | Journal article |
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Springer
2016
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| _version_ | 1797105516525125632 |
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| author | Bick, C |
| author_facet | Bick, C |
| author_sort | Bick, C |
| collection | OXFORD |
| description | The notion of a weak chimeras provides a tractable definition for chimera states in networks of finitely many phase oscillators. Here, we generalize the definition of a weak chimera to a more general class of equivariant dynamical systems by characterizing solutions in terms of the isotropy of their angular frequency vector—for coupled phase oscillators the angular frequency vector is given by the average of the vector field along a trajectory. Symmetries of solutions automatically imply angular frequency synchronization. We show that the presence of such symmetries is not necessary by giving a result for the existence of weak chimeras without instantaneous or setwise symmetries for coupled phase oscillators. Moreover, we construct a coupling function that gives rise to chaotic weak chimeras without symmetry in weakly coupled populations of phase oscillators with generalized coupling. |
| first_indexed | 2024-03-07T06:48:37Z |
| format | Journal article |
| id | oxford-uuid:fbb8ee0b-09af-43a7-afc7-6ff6944a4355 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T06:48:37Z |
| publishDate | 2016 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:fbb8ee0b-09af-43a7-afc7-6ff6944a43552022-03-27T13:15:53ZIsotropy of angular frequencies and weak chimeras with broken symmetryJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:fbb8ee0b-09af-43a7-afc7-6ff6944a4355Symplectic Elements at OxfordSpringer2016Bick, CThe notion of a weak chimeras provides a tractable definition for chimera states in networks of finitely many phase oscillators. Here, we generalize the definition of a weak chimera to a more general class of equivariant dynamical systems by characterizing solutions in terms of the isotropy of their angular frequency vector—for coupled phase oscillators the angular frequency vector is given by the average of the vector field along a trajectory. Symmetries of solutions automatically imply angular frequency synchronization. We show that the presence of such symmetries is not necessary by giving a result for the existence of weak chimeras without instantaneous or setwise symmetries for coupled phase oscillators. Moreover, we construct a coupling function that gives rise to chaotic weak chimeras without symmetry in weakly coupled populations of phase oscillators with generalized coupling. |
| spellingShingle | Bick, C Isotropy of angular frequencies and weak chimeras with broken symmetry |
| title | Isotropy of angular frequencies and weak chimeras with broken symmetry |
| title_full | Isotropy of angular frequencies and weak chimeras with broken symmetry |
| title_fullStr | Isotropy of angular frequencies and weak chimeras with broken symmetry |
| title_full_unstemmed | Isotropy of angular frequencies and weak chimeras with broken symmetry |
| title_short | Isotropy of angular frequencies and weak chimeras with broken symmetry |
| title_sort | isotropy of angular frequencies and weak chimeras with broken symmetry |
| work_keys_str_mv | AT bickc isotropyofangularfrequenciesandweakchimeraswithbrokensymmetry |